Magic State Factory Catalog

[\![428,\,80,\,4]\!] factory

\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{}\cdots

distance, proved here
d=4
error coefficient
A_{4}=7{,}936
\gamma_\rho
1.2098
V_{\mathrm{ex}}
80
wires
N=100
Clifford correction
none with T powers
found by
AI search pure T

The circuit

The 100\times428 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.

  • output wires
  • check wires, measured and postselected
wire
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420
out 0 (189)····1·11·1····11··1··111·11··111····1·1·11·11···11·1···11··1··1···11··1····1··1······1·1·1···1··1·1·11···111·1·1·1·1··11·1···1·11111·······1·1·11··11111111··11··1······1·1··1···1111·11111··1111111··1··1···11··1·11···1··11···1··11111·1·1··1···1·1··11··1·1····1·1·1····11·1·····1···1·1·1·······1···11··1·1·····11···11····11·1··1··1··1··1·11·1···1·11111········11··11·111111·11··1··1·····1·1··1··11111··11111···1111·1·11··1·1···11·
out 1 (167)···1·11·1····1······11····11····1··11111··1···11·1···1·1··1·1·11·1··1·11·11·1·111··1·1·11·····1···111·····1·1·11·1········1·11·1····11···1···11·1·····1····1··11··11··1······1····1·1111111···1·11···1···11·11·11·11··11··1·······11···11······1·1111·1··1······11··1····1·1·1··1···11·1···1111··1·11111111·····1····1·1·1······1··1···11··1········1·11·1····11····1··1·1·1····1·····1·11··11·1······1···1·1··111111····1·1·1····1··11·11·1
out 2 (173)···1·1·11···11··1·1·1111·····11··1·1·1111···1·11···1····1·11···1·1111·11·11···1·1··1···1·····111··1··1··11·1··11·1·····1··1··1··111········1·11···1·1·1·1·1··1·1·1·1··1···111···11··111·11···1··11·1·····1···11·1·1·1··1·11···1·1·1111···1·1····11·11·11·····1··11····1·····111······1·11·11111··1··1·11·1····1·1·1··1····1···11··1····11··1·····1··1··1··111·········11·1··1·1·1·1··1···1·1·1·1···111···1··11·11·11····1··1·1··1····1···11·
out 3 (171)·····1···1······1·········1··1·1·1·11···111·1···1···1··1·1111···1··11··1·11·1········1·11···11·1··11·····1···1··1··1··11·111·11····1·1·11··1·1111·11·111·11··1111·1········1·1·1··11111······1·11·1·1·1··1··1111··1·····1·····1········1·1····1·111····111···1····1·····1··1·11·1·····1···11·11··1·1····111···1···1··1·11······1·····1····1···1·11·111·11····1·1·11···11·11111·111··11··111·1·······1·1·1·1111·11·······1·11···1·1·1·1··1111
out 4 (189)·····1·11····1···11···1··111··11111··111·1··1·1·1···1···11·1··11·1·1···1·1··1·1······1··1···11··1···11··1·····111·····11·1·11·111111111111···1111····1·111·········1··1·11···1·1·1111··1111···1111111·1··11·11····1·1··1··1····11···1·111··1··111··11·1·1····1··1·1·····1···1·1·····11·1··1··11····11···1·1···1·····1····11···1········11·1·····11·1·11·11111111111·1··1·111···1·11·1········1·1·11···1·11111····1111····111·1·111·1·11·11··
out 5 (191)···1111·····11111·1···11·11··1···1··111·1·1·1·1·1·11·1··1·11··11·1·11·11·1·····11·······11···1·11·1·11·1·111··1·11··1·11··11·1····1··1·1···1·11·1·11·111··11···111····1··1·111···1···11··1···111·1········1··1111111·····1111·1·1···1111·1······1·111··1·1···1··1·1··11··1··111·····11·1··11111······11···1·1·1···1·111··11··1·11·1····1··11···111··11·1····1··1·1····11·1·111·111···11··111···1··1·111··1·····11··1····111··1········1··111
out 6 (163)·····1··11···1·11·1······1···11·1··1·11111·11·····1·1····11·1·111··11····1···1··1··1·1······1·111··11··1·····1111··11····111··111···11··11·1··11··1·1···111··1·1··11··1··1·1·1····11······1···11·11·1·1······1····1····11·1·1·1·1·····1··1·1···1·1·11·111··1·1·······1··1····1··1···111···11··1·······111·······1·1·1··1·1···1·······1·11·1···11···111··111···11··1·1·1··11·1·1···1·11···1··11·1··1·1·1···11·1······1····11··1·1·1·1·····1··
out 7 (171)···11····1···111··1·1········1111···111·11··1···11··1····1··1··11·11··11·1······1··1·1·111··1·1·1··1··1·1····11····11··1·111··1·1···11·111·1··11···111···111·11···1···1··11·······111·····11····111·111··1··11·111······1·111···1·1······1·1··11··111··11····1····1·1···1·······1····11·1·1·111·······11111·1···1···1··1···1··1······1·1······11·1·111··1·1···11·11·1·1··11··111····111·1···1··1··11······1111······1······1·1·1·111·1··11·1
out 8 (173)···1···11····111·11··11······1···1·111·1·1·1··1·1····1·11·1···11111···11··1·1··1········11···1··1···11·111····11·1····1··11····1·11··1·······1·1·····1·11111·1111··1··1··11·11···1·11··1··1··1111·11·····11·11··1···1··1··111··11··11····1······1111··1·1··1····1·1······1·111······11111···11···1·1·1····1·1·11····1····11··111·······11··1····1··11····1·11··1·······1··1····1·11·111·111··1·1··11·11··1·111···1··1···1111···11····11·11··
out 9 (205)···1·1111···1·1·1·1·11·1·····1111··11··111111·1111111····1··1··111··1·1·····1··1·····1·111··1··1··11···1··11···1···1··11·11··11111·11··111·1··111·1·1111111·····1111·····1·11··1··111111·····1·1··111·1··1···1111·111··1·1·1··1·1·11·1···1·1··11·11···1111·1·1··111·111·1·······1····111···11······1·1··111·1·····1··1·1·····1··1·1·····1·····1·11·11··11111·11··11·1·1··1111·11111·11····1111··1·1·11··1·111··111······1·1····111·1·1···111
out 10 (147)·········1··1·1···1···11··11··1111····1·11·1···1·111·····1·11·1·1111···1·1·····1···1·11·11··11··1··1···1·1·1·1·····1··11····1··11··11···1··1·1·1·············1··111······11··1·1·1·····1·1···1···1111·1·····1·1·········11·1····1···11·11··1··111···1··11··1·····1··111·······1·1···1·111·1··11······1·11·1·1·1·····1··1·····1·1··1··1········1·11····1··11··11···1···11··1···············111·····11··1·11···1···1·1····1····1·111·1····1·1·
out 11 (157)···1········1·1·11····1···11·1··11····1··1111··1·11·1··1111·1···1111··1···1·1·1·1······1····1···1·11··1·1·1····1·111·····1··1111·11··1···1······1·····11·111··1···1········11··1·1·1·11111··1··1··11·1·········11········1·1··11····1··111·····11···1···1111·1···1··11··1··111··1·····111·1·1····1·11·1··1··········11·1···1··1·1·······1··11·1····1··1111·11··1····1······1····11··111·1···1·······11··11·1···11111·1····1····11·1········1
out 12 (197)····1··111··11·1·11·1111·111·1·1·····111111···11··11···111·11··1·11·1·11·1··1·1···11·1·111··1·1·1··1·1·1···1·1111·····1··1111····111·1·1···1···11··11··1·11···1··111··1·1·1·1··1·1·1····111·1·····111·1···1·1·11·1··1··1111·1··11·11111111····1····11·1111······11···11····11·1·1····1·11··1111····11··1111·1···1···1··1··1··1····1··1·11·1·····1··1111····111·1·1····1···11·11··1··11··1··111·1·1·1·1··11·1······1111·········111·1··1·1·11
out 13 (159)···1·1··11··11··111·11·1·11···1··1··1111···11··11·11········1··11·111··1··1·1··1·······1·1········11···1·1·1·111···11·1···1··1··1····1·11·····1·1····1111········111··1·1·1·11····1··11··1···1··1·········1·111·1·1····1111···111·11·111···1····1·111·1····1·1···11··11·········1····11·1·11·1···1·1·1···1··1········1·1·····1·1··1··1·11····1111···1··1··1····1·11······1·1···1111········111·1·1·1·11···1····11··1····1··1··········1·111·
out 14 (157)···1··1111··1·····1··111··11···1····1·11·111··11···1·····1111···111·····111····1·····1·11···111·1······1·111·1·111·11·11··1·1··1·1·1····1····1·11·······1······1·111······1·1··1····1··1·····1·1·11·1·1··1···11·1··11··111······1··111·11·····1···1·1·1·11·1····11····1······11·1·····111·····1··1···1··111···1·1···1········1·11·1··1··1·11··1111··1·1··1·1·1····1····1··11······1······1·111·····1·1··1···1····1······1·1··1·1·1·1·1···11·
out 15 (147)···········11·1···1··111··1··111·1····1·11··1··1·111·1···1··1·1·11·····1·1·····1···1·1···1··11·····11··1·1·1··1····1··1·······111··1····1··1·1111··········1·1···11······1··11·1·1·····1·1···11·11111·1···1·1·11·········1·1····1··111·1·1·1··1·1···1··11····1···1··111··1······1···1·11·····11······1·11···1·1········1·1···1·1··1····1······1·1·······111··1····1···11·111··········1····11·····1··11·11···1···1·1····11·1·1·111·1··1·1·11
out 16 (167)·····11·····111·11··1·11·11··1···1·111111·1·1··1·111····1··1··111·1·1·11·1·····11······1·1···1·1··11·1··1111··1·1··1···1··11·1····1··1····11·11·1·1·1·1···1·····11····1·1·11·1···1···11··1···11·11··········1·1···11·····111··11··1·1111·1······11111·11·1···1···1··111·····1·1·····111·1··1111······11··1··1·1···1··1·1··1···111·1····1··1···1··1··11·1····1··1······11·1·11·1·1····1····11···1·1·11·1··1·····11··1····11·1·1··········1·1·
out 17 (171)····1········11·1··1·1·1·1······1··1·1··111··11·1··11111·1····1··11···11·11········1·1·1·1··11·11·1·1111·11111···1·11··1···11·11·111··1·······111··1···11·11·11·1··1·11··1·······111·1··1····1111····1···1·······1········11··1··1·1·11········1·1·1···111····1·1·1···1·1111········1··11···111··1·····111··1·1···1·11···111·1·11·11·1·····1··11·1···11·11·111··1········111·1···11··11·1·1··111··1······111·1·1··1·····11111·····1··1······
out 18 (149)····1·11·····111·11·111··1···1··11···1·····1··1··11···111······111·11·1···1·1·11·······1·····1··1····1···1····1·11·1···1·11····1111··1·1·····1·····1···1·11··1111·····1·11··1····1·1···1··1·11·····1······1··1·1·1·11·····111··11·111·1··1·····11··1·······1····1···11····111········111··111····1·111···1····1·····1·····1·1··1·······1··11··1··1·11····1111··1·1·····1·····1···1··11··111····1·11··1···1·1·1···1··11··1·······1·····1··1·1
out 19 (173)····11·11···11·111·····1·11··1·1·1··11·1·111··11···1···111·····1···11··1·11···11···1·1··11··11·1··1··1·1·1·1··1111····11··1··1···111···111···1·1··11··11··1···1·11·1··1·1····1·1·····11·1·1····1··1·1·1···1·1·1··11·1··1·11·1·11·····111·1····1·1·11··1·11·1····11····1····11········1···111·11··1··11·11·1·1·1···1··1····1··1·1··1····11·11····11··1··1···111···11·1··1··1·11··11···1··1·11·1·1·1····1·1······11·1·1·····1····1·1·1··1·1·1·
out 20 (197)····11111····11111···1111·11·1··1··1·1·11·······11111··111111··1··1···1·······1····1········1111··11·1·1·111··1·1··11·11·11111···11·11···1·1·11·1·11·111······11·111··1··111·1···11·111·111··1·111·11····1····1··1111··1··111·11···111·111·····1·1·1··11··········1·111·1··1111·1····1··1···1·······1··1······1·1·1··1·1··1··1·11·1····1··1···1111·11111···11·11····1·11·1·111·111······11·111·1··111·1··11·1··11·111···1·11·1··11···1····1·
out 21 (149)···1···11···1··1··1···1···1··1111··11·11·11···11····11·1·1··1·1·1·····1··11···111··1·1·1··1·1······11···········11·11·········1·11·111·1·1···1·1···1····1·11··1·1·11········1··1·11·····1·1··111·1··1·1···1····11···1··1·1··1···1···1··1·1·1··11·11·1·1·11······11······11·1····1···1·1·····1·1··1··111111·············1·1················11··11········1·11·111·1··1··1··1··1····1··11·1·1·11·······1··111·······1·1···111··1···1·1··1····1
out 22 (175)···1·11··1··11··11··1111·11··1··11·1111·1·1····1·1·1·1··1··11·111···1·11·······1·······111···1····1111·11111·11····1······11·1····1·11·····1·11···1·1·1·1·11····111···1·1··1·1···11··11··11··11··1··········1·111·11····111···11··111111·1·····111111··1·1·······1··1·1··1··1·1·1···111····111·······1···11·1·1······1·1·11··1111·1··1·1······1·····11·1····1·11······11·1··1·1·1·1··11···111··1·1··1·1··11····11··11···11···1······1···1·11
out 23 (179)···1··1········11····111·1···11·1··11·1·1·11··1··111·····1·11·1·11111·1·······111··1···11···1··11·111····111···1·1··1··1·1·1·11·1···11·1···1··1···1·1·11·1···1··111·····11111··1·11111·1111···11···11····1····1·1··1········1·1····1111··111···1·11·1··1·1·1····1···111·······1·1···1·111·111·······1111·11·······1·11·1·1·····11·1·····1··1···1·1·1·1·11·1···11·1····1··1··1·1·11··1·····111····11111··111111·1·1111····11·····11···1····1·
out 24 (165)···1·11··1·····1111·1····111··11·1···1···11·1·1·1·1····1·11········1···1·11·1········1··11··111·1·11··1··11·1···11····11·1··1··111·1·1·1·····111·····111···1··11··1·····1··1·1····111·11·1·····1111·1·1··11·1···1·11····1···1·111·1···111··1··1·1··1····11···1··1·1··1·····1·1····1·······1··11··1·1····1·1·1·1·1···11·1···1···11··1······11····11·1··1··111·1·1·1·····1·11····111····1·11··1····1··1·1···111···11·1······11·1·1·1·1·11·1···
out 25 (181)···111·11····1·1111··11··1·1·1··1··111·1······1·1·1·1··11·1···111111·····11·1·1·········11···1·1··1·11·1······11·1·1···1··1·11·1·11·1········1····11·11··1···1111··1··1·111111···11··1·1111··1111··1·1·······1·1111·1··1··1·1·111··11·1·11·····1·111··1·········1·1··1·11··111······11111·1···1··1·11·····1·1·1···1··1···11··1·········11··1··1··1··1·11·1·11·1········1····11·11···1···111··1·1·111111··11··1·1·1111···1111····1·1······1·1
out 26 (111)···11··11·····11····1····1·······1·11··1··1·····111··1·1··1···1···1····1·······1·······111····1·····1···1······11···1·11·········1·····1········1··1·1··1··1···11··1·····11··1······1·········111··1·····1··1··111··1··1···11·····1···1·········111···1··1········1·11···1·1·1······1···1····1·······1···11·1···1········1····1·········1·1····111·········1·····1·········1·1·1··1···1··11··1····11··1·····1·········1··111····1····1··1··1
out 27 (179)····1·1·····111··11·1··1·111·1·111···11·······11·1·1···111·11··11·11··11·1··1··1·····1·111··1·1·1··1·1····11··1·11·1··11·11·1·····1111·11····1··1··1·····11··11·111···11111·11·1···1·····11···1··1·11·······1111·1·1·····111···11·1··11111····111··11···········11··1·1····11·1·1····11·1·1·111····1·1··111·1···1···1··1··1·····1·1····1··11··1·11·11·1·····1111·11····1···1·1······11··1·111··1·111·11·1··1·1·····11····1···1··11······1111
out 28 (189)···11111·1····11··111·11···1···111·11···1·1·111··1·111·····1··1·1111··11····1·11·······111·····1····111·1··1·1·11··1··11···11·1····1·1·1·1·1·1111·111···1····111·1······1·1··111·11·····11··1·11·1···11·1·1·111111111···1··11···111·11··1·····11111····1·1···11·1···1·1·11····1·····1·111·1·11·····111···11·1·····1······111··1···1··1··1·1···1·11···11·1····1·1·1··1·11·111111···1·····11·1·····1·1··11111··1····11·1···11··1····11··1·1111
out 29 (143)···1·1········1·1·1·1·1····1·11·11·1··1···1·1··1111·1·····1······11·1·1··11·1··1·······1·1···1·11·1····1·1······11·······1·1111·1···11·1·1····1···1··111·11····1··········11·····111·11··1·····1·1·1···1·····1·11·1········1··1·1·1·1···11·1···111··1····1···1···11·11··1····1·········11··11·1··1·1·1···1··1·1···1·11·······1·1··········11·······1·1111·1···11·1··1····1··1··111··11···1·········11····111···11··1······1··1··1········1·1
out 30 (63)···1··1··1··1·1···1··1····1···1··1··1···1·1····1·1·····················································1··1··1·11···1··1···1····1····1··1··1·1·1····1··1························································1··1····11·1····1··1···1···1····1·1····1·1··1····1··1························································1··1····1··1·1····1·1···1····1····1··1···11··1···1··1··························································
out 31 (175)····1···11··1·1·1··1·11··111····1··11··1·11··111··1·1··1··1···1·1·111·11·11·1··11····1·1·1······1·1·11111·1··1···1·······1··1111·1·····1······1·······11·1·1·······1·····1111111·11111·1··1·1111··11·1···1··11···1·····111·1··1··1·11·111······1·11···1·11····1·11···1··1··1·1······1·1·1·11111··1·1·11·11··1····1··11···111·11·1····1·····1·······1··1111·1·····1·······1······11··1·1······1····11111111111··1·1··11··111····11·1··1··11··
out 32 (183)···1·1111····1·······11···11·1··1··1111··11···11·1·111·1··1·1··111··1·11·11·1·111······11·····111·1111····1·1·1·11········1··1·1····1··1·1···11·1·1·1·1····1··111··1··1······1·1·11·11·1111···1·1·1··1···11·11111·111··1··1········11··111·····1·1111···11······11··1·1·11·1·1··1····111···1111··111111··11·····1·1·11·1·11·····1··1···1··11········1··1·1····1··1··1··1·1·11·1·1·····1·111··1·1······1·111·1··1·1111····1·1···1··1··11·1111
out 33 (143)···11·1······111·11·11···11··11··1···1·····1······1····11·1····111·11·11··1·1·1····1···1·····1·····1·1···11···1·11·1·····1·····11·1····1·····1·····11··1111···11······1·11··1······1···11·1··1·····1·····11·11·111·1······111··11·11··11·1·1····1··1·······1·········1·····111·······111··1111··11·11··1·1····1········1··1····11······1··11··1····1·····11·1····1·····1·····11··11·11··11·····1·11··1·····1·····11·1···1·······1····11·11·1
out 34 (181)···11··111···1·11111··1··1·1·11·1··11111··1···1·1·1·1··11·111·11111·······1···1·········1······1··1111·1·1···111·1·1·1····1·11·1111·1····1········11·11······111··11··1·1111·1···1···111111··11111·1···········111··1··11·1·1·1111··1·1·11·1···1·1111·1··1······1·1··1··1··1111·1···11111········1··1·····1·······1··1·1·11··1·1·····1·11··1··1·····1·11·1111·1·····1·······11·11·······11··11·1·1111·1··1···1·111111···1111·1··1··········1
out 35 (181)··1···11·1··11···1···1·1·111·111···1·11··1····1111·1·11111··1·11···11·11·11·1·1····1·1·1·1··1···1··111·11··1·11·1········11·1····11111··1······1···1·1···111··11111···1·1····1·1···1·····11·1·1·111·1·1·····111····11···111····1···1·11111·1··1··1·11···1·······111·1·1··1111···1···11····11111··1·11··111··1·······1··1·11··11···1··1·1··1········11·1····11111··1·······1··1·1····111·11111··1·1····1·1··1·······111···1·1·1·1·1·1····111·
out 36 (143)···············1··1····1···1·1··1··1····1·11·····1·111·1··1···1··111··1·······111··1····11···11·1···1··1·1·1···1····1·1···1·1·11····11·111·1·1··1··1···1··11··11·1·1······1·1·····1·1··1111···1··1·······11···11············1···1····1··11·····1·1·····1·1·1········1·1·11·1·1···1··1··11·1·1·······1111··1·1·1·1···1····1···1·1··1·····1······11···1·1·11····11·11·1·11···1·1···1···11·11·1·1·····1·1····1·1····1111····1···1·······11···11
out 37 (157)···1···11···1·11·····1·1··11····11·····11·1·1·1111111··11··1·····1·1···1··1·1·111······1·1·············1·1·1···111··1·1····11··1·1··11···1·1··1·1··111··1·1··11··1·1·····1··11·1··1···111·1····11··1·1······1·1·1···1··1·1·11······1·1·11······11·····11·1···1··111·111·1··11·1········1··1··1···1·1111··1··1················1·1··1·····1·11···11····11··1·1··11····1·1··1·1·111··1··1·11··1·1····1··11·1·1··1··111·1·····11····1·1·····1·1·
out 38 (165)······11·1··1·11·····111···1·11·11·1···1·1·1···1···111·1··1·····111···1·······1·1·······11···11····11····111·1·1···1··11··111·1111··11·1·1·····11··1····1·11·11111·1······1·1····11·1··1111·······1···1··11···11···11···11·11······111··11·1···111····1·1··1·····1····1·11·1·1········111···1·······1·1···1·1·1·1······1·1·····11·1·11··1·····1·11··111·1111··11·1··1·····11·1····1··11·1111·1·····1·1···11·11···1111··········1···1·11···11
out 39 (183)···1····1···1111··111·····1··11111··1111···1111·····1111··1···1·1······1·······1·····1··11····1·1·1·11111·1··11111····1·····1···111···1·1··1·1··1·1··1·11·11··11111··1···1111··1·11111·111····1·111·1·1·······1·1······1·1111···111····1·1·1··111·11111····1·11·1·······1111·1······1·1······1·······1··1·1·1···1···11···111·11·1····1·11·11····1·····1···111···1·1···11···11··1·11··11·11111·1···1111··11111··1·111·····1·1·1·1·1·1······1·
out 40 (167)········1···1·1···1······11··11····111·1·1111·1·111·····1··11·1··1····11·1··1·1·1··1···1·1···1·1·····11·11··1·1··1·1···1·1·1·1··111··1·1···1·1·11·1·11····11··1·1··1··1·1···11·1··1111··11····1···1···1··11·11·········1·1·1····1·····11·1·1·····111··1·11·1·1··1·1·11······1·1·1···1··1····111····11·11·1··1·1···1·······11··11···1···1···1··1··1·1·1·1··111··1·1····11··111·11·····11·1·1··1·1·1···11·1·111··1··11·····1····11···1·11·11··
out 41 (165)·1···1111····1·1111··11··1·1·1··1··111·1············1··11·1···11·1·11·1··11·1·1······1·1·····1·1··1·111·1·1···11·1·1···1··1·11·1·11·1········1····1···1·1····1111··1··1··1·11··1·11··1·1111···1··1·1·1·······1·1··111··1··1·1·111··11·1·11·····1·111··1·················1··111······11·1··111·1··1·11···11····1···1··1···111··1·1······11··1··1··1··1·11·1·11·1········1····1···1·1·····111··1·1··1·11··111··1·1·1111····1···1··1·1······1·1
out 42 (173)·····11111··1·1······111·1111···1··11··1·111··1111·11····1·11····11·1·····1·1··········1····111·····1·····11·1·1·1·1··11····11·1·1··1··111···1·11····1·11·1······111····1·1·11·1·11·1·11·1·····1111·1·1··11··111··111··111·1·······111111······1·11···1·11·1····111·1·1·1·····1·1······11··1·····1·1·····1····1·1········1······1·1··1··1··1··1·11····11·1·1··1··11·1··1··11···1·11··1·····111···1·1·11·111·1···11·1······11·1·1·1·1·11··111
out 43 (179)·····1··1······1111·1111·····1·1·1·11··1···1···111111··1·1··1···11·11·11····1·11·····1·11···1·111·11·······1·······11·1··1·1·111·1·1·1·111····1·1·1··11··11··1··1111····1··111·1·111·1111····1·1·1··1·······1·11··1····1····1·111·1111···1····1·111···1····1·····11·111·1··1····1·····11··1111·····111··111·····1·1·11·1·········11···········111··1·1·111·1·1·1·11·1····1·11··11···11····1111···1··111·1111·1·1111·····1·1··1···1······1·11
out 44 (175)···11··111···111·11·1111·1·1··1·11·11··1·11·1·1··1·111·11··1···11·11···1····1·111··1····1·····1·1··111·····1·11·······1··11·1·1·111·1···11·····1···1····11·1·····1·1··1··11··1···111····1····1·1·111··1···1·1·1·11··1··11·111··11·11111·1··1···1111···1·11···1··1···1·1·11·11·1······11·1·1··1·····11111··1·····1···1··1·11·······1··1·1········1··11·1·1·111·1···111·····1··1····1·1·1····1·1·1··11··1··111······1·····1·1··1·11··1··1·1·1·
out 45 (191)···1111111··1·111···11····11·11·1··1···111····11··1·11·1······1·1·11·····1··1·1····1·1·······1111·1·1···111··1····111··1·1·1111·11··11·11··1·1111·111·1·1111····1··1·····111·1·1··11·11·11···11··111··1···1·····11111··111·1111···11···111·1···1·1····111·······11···1··11·1········1·1·1·1···1····11··11·····1·1·1·11···1····111····1······1·11·1·1·1111·11··11·11···11·111111·1·1·111···1··1····111·1·1·11···11·11····11···1·11··1··1·····
out 46 (143)1····11·1···111··1··1··1·11······1·1·1111·111····111·······1···11·1·1··1·11····1·······1·····1····1··1···111··111··1··11··1··1·······1·····1·11·1···1·1·1·······11·1··1·1·1··1·······1···1···1··11···1····1·1·1···11···1·111···1··1··111········11·11·11·1·1·1······111·······1······11·1··1·11··1···1···1····1······1····1····11·1····11·1···1·11··1··1·······1······11·1·1··1·1·1·······11·1·1·1·1··1········1···1····1··1·1····1···1·1·1·
out 47 (163)···1111·····11··11·······1·1··11···1·1····1·1·11·········11·1··111·11··1··1·1··11··1·1··1···1111··11·11·1·1·1·11·······1··1·111·1··1·1·1·1·····1··1···1·1·11·1·1·····11·11·1·1·······1···11··1·1···1111··11·····1111·····11···11······1·1··1··1··1·1·····1···1··11···········1··1····111··11·1···1·1·1111·1···1·1·1··1·1··11··1·1··1··111········1··1·111·1··1·1·1··1·····1·1···1·1··11··1····11·11·1·1······1·1···11···1·1·····1111·11·····
out 48 (165)···11·111···1·11··1·11·1··11·11·11·····11··11·1111111··1··11·····1·11·11··1····11······1·1·1·1·········11111···111·········11·1111··11···1·1·1··1··111··1·1··111·1·1·····1··1·····1····1··1····11···········1·1·11·11··1·1·11···1·11·1·111·1···11·····11···1·1··111·111·1··1·11········1··1111···1···11··1··1·1··············1111·1·····1·11·········11·1111··11····1·11···1·111··1··1··11·1·1····1··1····1··1···1··1·····11············1·1·
out 49 (167)····11······111·111···11·11··1···1···11···1·1···1··1·11·1·1···1111·1··11·1·····11······11····1·1··1·11···1·1··1·1··11·11··11·1····1··1·11····11·1·1··1111·111··1·1····1·11·11····1···11··1···11·············1111·11······111··111···1111·1······1··11····1···1····1···1··11·11······1111··1·111······11··11···1···1··1···11····1··1····1··1···1111··11·1····1··1·11····1·1·11··1111··11··1·1···1·11·11···1·····11··1····11··············1111
out 50 (181)·····11111···1·1111·11·1·1···1·····11111·1·····1··11····1·11···1·1111·11·11···1·1··1···1·····111··1···11111·111·11·1·········111·11··1111·····1·1·1···1····1·1·1··11··1·11111·······11·111······111·······1··11···111··11·1·1·111·11·11··1·······1111·1·1········1···11·····111······1·11·11111··1··1·11·1····1·1·1··1·····1·1111··1·1·1··11··1········111·11··1111······1·11···1·····1··1··11·1·11111······11·1·111···1···1·1·1······1··11·
out 51 (189)···111·1·1···1·1111···11·11··111·1··11·····11··1···11··1·11···111··11·1··11···1····111·1·1··1111···1111·11··1111·1····1··11····111·1··1··1·····1··111··1·1·1··111·1···1·1··1·····1·1··1111···11·11··1·1··1··111·111·1···1·1·1·111···1111·1·1··1·1·11·······1·1···1····1·1··1·1······111···111·1··1··1··111··1·1·1·1····1·111··11···1·1·11··1····1··11····111·1··1···1·····1·111··1··1·1·111·1··1·1··1····1·1····1111····11·1·1···1·1·1··111·
out 52 (197)···111·111··111·1····111··1····11··111·1·1··1·1·11·11··111111··11···1·········1····1·1·111··1111··11·1···1·1·11111··1·11··11·11··11111··11··111···1··1111·····11·111··1·11·1···1·11·111·111········11····1····1·111·1··11111··1····111·1······11·111··1·1····1··1·1·1·1·1··1111·1····11····1········1··1111·1·1·1·1··1·1··1····1··1··1·11·11···111··11·11··11111··1·1··1·1··1··1111·····11·111·1·11·1···111·1··11·111···········11···1····1·
out 53 (163)·····11········11········11··111·1·11····11···1·1······1·11111··1··11·11··1·1···1······11···1··1··11·····11·····11·1··11·1·1·11·1··1·1·11····111··1··111·1···1111·1···1····1·1·····1111···1····11·1·111··1··11·1··11········1·1·······11·1·1··1·111·····11······1·1········1·11·1·····1···1111···1·1··1··11·······1··1·1·······11·········11··1·11·1·1·11·1··1·1·11····1·11·1··111··1···111·1··1····1·1····111·11···1·····11···1·111·1··11·1
out 54 (183)····11······1111111·1·1···1··1111···11····1·1··1··1·11·11·11···1·1111··1·1··1······1·1···1····111·1··1·1······111··11·11··11·1·11·1111·11····1····111·11···1··1111····1···1111···11·11·1··1····1·1·······11·11···11······1111·111·1·1··1·1·1··11··11·····1···1···1···1··11·11111·····1·11·11·11····1···11···1···1·1·11····1··1·········11·1···1111··11·1·11·1111·11····1····111·11····1·1111···1···1111··11·1··1·1··1·····1··1·······11·11··
out 55 (147)···1111·····11·11····1···111·11······11···1·1·11·········11·1··11···1··········111·1········1111··11··1·111···11·······1··1·111·1··1·1·1·1···1····11··1····1·111··1···1·11·1·1·······1···11··1·1····11····1··1··1111·····11·1·1····1··1111·1·······11····1···1··11···········1··1····11····1·········111······1·1·1··1·1···1··111······11········1··1·111·1··1·1·1··1··1····11··1·····1·11··1··1·11·1·1······1·1···11···1·1······11···1··1··
out 56 (179)···1·1·1····1·11·11·1··1·1·1·1·11··11···1···1·11111·11··111·1·····1·1·11·11·1··1···1···1····1···1·1·11··11·····111·11·1111··11···11111·11··1····1···111·11·1·1111·1·······1··1·1··1111····1····1····1····11·1···1·1·1····1·11··11·1··11·11····11·11····1·····1··111·11··11··11··1·······1··1111··1·1·1·1·1··········11···11···11········1·11··1111·1··11···11111·11···1····1··111·1·1·1·111·1······1··1·1·1111·1····1·····1······1···11·1···
out 57 (173)···11·111···1··1····1·1···1·····11·1·1·1111···1·111····1··1·1·1··1·1·····11···111··1··········11······111·1·11··11·11······1·1·1····1···1··1·1·11·1111·111·1·1·11··11···11···1·1·11··1·1111··111·11···1···1····111·11··1·1··1·····1·1··1·······111·1··1111······1·1·11·····1·1··1···1··1··1···1··1··1111········1·1········1·11·1··1·1····11··11·····1·1·1····1···1···11··111111·11·1·1··11··1···11···1·111··1·1·1111···111··1·1···1··1····1
out 58 (159)····111······111·11·1····111··1·11···1·····1·········1·11·11···111·11·11·11·1···1··1···1·····1··1··111·1··1···1·11·1···1·1··1·111·1·1··1·····1·····11·11·111··111·····1·11··1·····111··1·····1·····1·····1··11···111······111··11·1···111··1···11··1·······1·······1·····1·1111······111··11111··1·1··11·1····1·····1··1·11··1··1······1··11··1··1·1··1·111·1·1··1·····1·····11·11··111·111····1·11··1····111····1······1·······1····1··11··
out 59 (149)···1·········11··11··11··1···111·····1···1·1·11··11··1··1·1····1111·1·1···1········1···1······1·1····1··11····1··1··1·11·11····11·11·1·1·······111·1···1·111·111······1···1·11···1·1··11··1··1····1··11···1··1·11·········11···11··11·1··1·1··1····1····1··1··1·1···11···1··11·······1111··11····1·····1·1······1···1·····1···11·······1···1···111·11····11·11·1·1········11·1···1··111·11·····1···1·11··1·1·1··11··1···1······1··11··1··1·1
out 60 (171)····1·1·11····1·····1·1···1····1·1·11·11·1111··1··1·11·111·11·1·11·····1·1··1···1····1···1··11·····111····1··1·1···1··11·11··11···11·1·1·1···1111··1··11·1·1·11·1·11·····1··1····11111·······11···1·111··1111····1·1···11··1······1·1··1······1·111·1·1·11·1·1···1···1··11·11·1·1···1·11·····11····1··1·1···1·1········1·11·····1····1··1·····1·11·11··11···11·1·1··1··1·111·1··11··1·1·1·1·11····1··1···11111·1········11·····1·111·11·1···
out 61 (189)···1·1·111···11·11···1·······1·····1·11111·11·1··11·····111·1·11111·1·11··1·1·1·1······111··1·111·11·1·11····111·1········11·1·1·11·····11·1··11··1·1·1·1·1····11·11··1···1111·1···111·111···11·1·1·1·1··1··11··1·1·1··11·11··11···1·····1·······1·11·111··1·1··1···11······11··1···11111··111·1·1·11·1··11·1···1·1·11·1··1··11······1·11··1········11·1·1·11·····1·1·1··11·1·1·1·1··1···11·11·1···1111·1··11··1·111····11·1···1·1·1·1··11··
out 62 (179)···11····11·11·1111··1·1·····1··1····11···11··11·1·1·1·1·1·1··11··111·11··1···11············1··1··1·11111··1111·····1·1···1··1·1····1···11·····1··11··111·1··11·111··11··111·1····1·111111····11···1111···1··11111······111·1·111··1·1···1·····1···11····1·1····11··1·1··1·1··1·····11··1·1111···1··11············1··1···111·11···11·1·1·······11···1··1·1····1···1·1·····1·11··111··1··1·111·11··111·1···1·11·11111·····11·····1111··1··111
out 63 (143)···1··1··1············1··111·111·1·1····11··1·1·111··1·····1·······1··11··1·1··1·····1··1····11········1··11·1··11·11··1····1·1·1··1·1·1···1·1·1····11·····1····1·······11···1·1·1··1·1··1···1··1·11·11··11·11··1··1·1··1···········1·1111·1··1·11·····11····1··1·1·11···1····1···········1·11···1·1·1··1·1···1·1············1··1·1··1····11··11·1····1·1·1··1·1·1····11··1···11······1···1······11···1·11··1···1··1····1··1···11·11·11·11··
out 64 (155)········1····1·111··11···1····1111··1111·1·····1111··1···1····11·1·1··········111··1·1···1··11111···1··1·1····111·····11·111···11··11··1·1·····11····1·111·1·1·····1··1·1··1·······1···1111···11··1·111················1··1·1·11··11··1····1··111·111·1·1······1·11·11···1··········11·1··1·········11111···1·1·1·1·1····1···1·1·······11·1·····11·111···11··11··1··1·····11···1·11·1·1······1·1·1··1······1·1···1111····11····1·111········
out 65 (175)···1111·····11··11····11·11··1···1··111·1·1·1··111·1·1··1·11··111·····11·1·····11·······11···1·1··1111·1·111··1····1··11··11·1····1··1·1···1·11·1·1·111·1·11···111····1·1··1·····1···11··1···111·1·······1··1·111111·····11···11····1111·1······1·111··1·1···1···11·1·1··1··111·····111·····111······11···1·1·1···11·1·1·11··1·11·1····1······1·11··11·1····1··1·1····11·1·11·111·1··11··111···1·1··1····1·····11··1····111··1·······1··1·11
out 66 (195)···11111····1·1·11···111·11···11·1·1·1··111·1···1·1111·111····1··111·····1·····11··1·1·1····111···111111·1111·1·····1··1······111·11···111···111···1·11·11···11·111···1·1111·1···1··1·11·1···11·1·1·1·1··1···11·11111····1·1··11···11111···1··1·11·1···111···1····1··11·11·11·······1··11·1···1······11111···11·1····1·1·111·1·11·11···1·······1·1······111·11···11·1··1·11··1·11·1·1···1·111··1·1111·1··1··11··11·1····11·1···1·1·1·1···11·
out 67 (159)·······1·1····11111··1·1··1··1·····11···111·1··1·11·1···1·1···1·11····1··1····111····1·······111···1·1··11·1·1·1····1··1··11···1·11····1·1·1·1·1··111··11·····1111·········11··1····1·111····11·1·1··11··1···11·····1···1··11·111··1·1·1·1·······11····111···1···1··11··1···11······1·11····1·1·····111·1·····1·1·1····1··1···11··1··1··1······1·1··11···1·11····1··1·11··1·111··111····1111········11··1···1···111·····11·1···1··11·1···11·
out 68 (205)···111111···11·1··11·1···1·1·111····11·1·····1·11·1·1111··1···1·1·1·1··1·11·1·111··1···11····1··1··1111··1··11·1····1··1·111·1··1·1·1·1111·1··1·1·111·11·111·111·1···11····11··1·1··1·11··1···111·11111······11111111··1·11·1···11·1··1·11·1··1···11··1·······1··11··1··1111·1······1·1·1··1·11··1·11111·111··1·····1··1·111···1···1·1··1······1·1·111·1··1·1·1·111·1·1··1·1111·11··111·11·1··11····11··11··11··11··1····111···11111·····111
out 69 (141)······11······1·1····11···11···11·····11·11····11·111··1·1·1·····11····1·1··1··1········11··11·······1·1·1111·······1·1····11·11···11··11··············11········11·····1111·1·1·11····1·1···11···1111····1·1·1····11······1··1····11··11·····11····1·1·11·······11··11·1··1··1········11····11····1·1····1·1·1···········1··1·11·11···········11····11·11···11··11··············11········11····1111·1·111······1·1····11·····1111···111·1·
out 70 (171)···11111·1····1······111··11·11111·····1····1·11·1··1··1·1····1·····1·····1·1···1··1·1··11··1·11111··1·1111·11·111·11·11·1·111··1··11··1·····1·1··11·111·1···11·1·1······1··1··1·111·1····1·····1··11·1········111111···1··1·······111·111·1··111·····1······1··11··1···1··1········1······1·····1·1··111·1·1···1·1·11····1··1111··1·1··1·11··1111·1·111··1··11··1·····1··1·11·111··1···1·1·1·····1··1··1111·1·1····1······1····11·1·······1
out 71 (159)····1···1·····1······11··111·11111··1·11·111··11··1·11··1···1·1··1·····1·11·1··11····1·······1··1·1·11·········1···1·····1··11··1·1111···1···111······11·1·1······11·1··11··1····11111···1···11··11··11··1··11···1·····1···1·······11·1111·1··111·1·1·1·11·1····11···1··11··1···1··11··1·····11··1·1·11·1·····1·····11···11·············1·····1····1··11··1·1111····1··1·11·····11··1·1·····111··11··1···1111··1···1····11···1·1··11·1··11··
out 72 (151)···1·1···1···1····1·11·1·1·1·11····1·111···11··1··1····1···11··11·1·1·11·1···········1·1·····1·1··11·1···1·1111····11·····1··1··11·····11·····111·1···11··1·····11····1·1·1·11·······11··1···11·11···11···1·1···1·1·····1·1·····1·11·11·11·1·····1·11·1····1·1···1···1·····1··1·1····11·1··1111·········11····1···1··1·1··1····1··11·1·1······11····1··1··11·····11······1111···11···1····11···1·1·1·11·······111··1····11·1·1····11··1·1···
out 73 (163)···11111·1··11··1·1·1·1··11··111····11··1···1·11··1··1·1·111···1····111···1···1········1····1·111······11·1··111·1··1·1··111··1111·1···11··1······111····1·1·1·1······1··1·1·111·1·1···111···1······1·····1··1·111111···111···1·1·1·1·11·1·1··1···11···1·····1··11···1···1·1·11······1·····11····1··1····1······1·1·1········11·1····1·11··1···11··111··1111·1···11···1·····111·····1·1··1·····1··1·1·1111·1·1···111····1········1····1··1·1
out 74 (155)···111·111··11··1·1·······11···11··111·1·······1·1···1···1····11··1·1··1·1··1·1······1···1··11····1·111·1·1··11··111··11··1·111····1···········1···1··1···1··1·11··1··1··1·11··1··1·11··1···1·11·····11··11·1··1111·1··1111···1·1······11·····11·111··1··········1··1····1··········11··1··1·11····11···1···1·1······1···111··1·1····1·1···11·1·11··1·111····1··········1·1··1··1····1···11··1·1··1·11··1·1·11·1··1··1···11·······11·11·1··1
out 75 (171)···1··1111··1··1·11·······1···111···11111··1···11·1·1··111·11·11·111·····1··1·1·1····1··11··111·1····1·1111··11····11·1··1····1111111··1·1·1····1····1··11···1····11··1···1·1··1··11···111····111···1··········11··11··111··1··11······1···1··11··111·11···1·····11··1··1··11·1·1···11·11·1···1····11·1·1·1·1·1·1···1·····1··1111····1·1·1····111··1····1111111··1··1·1····1···1··1·1·······11·1···1·1··1·11·1···111·····111·····1·········1
out 76 (167)···1····1···11·1111·1·11·111·1··1····1·11···1··11··1·······1···11······1····1·1·1········1···1111······1···1··11···1···1·1111·1···1·1··1·1·1·11···1·11·111······11·1··1·11·1·1·1·111··1·1·1··1·11··1······1·11111······1·11·1·111·1·111111···1·1···1··11·····1···11···1·······1······11······1·····11·1·····1·1·1·1·1········1····1····11·····1··1·1111·1···1·1··1··1·11·1··1·11·11·1·····11·1·1·11·1·1·1111····1·1·1···1·11····1·····1·1111
out 77 (197)····11111····11111···1·1·11···1111·1·1·11·······11111··111111··11···1·········1····1·1·111··1111··11·1·1·111··1·1··11·11···1·11·11111····1·1·11·1·11·111······11·111··1·11·1···1·11·111·111········11····1····1··1111··1··111·11···1·111···1··1111·1··11··········1·111·1··1111·1····11····1········1··1111·1·1·1·1··1·1··1··1·11·1····1··1···11111··1·11·11111·····1·11·1·111·111······11·111·1·11·1···111·1··11·111···········11···1····1·
out 78 (181)···1·····1··11·1·····111··11·1111··1111·11····1111·1·1··11111·111··1··1··1··1········1······1···1··111·11··1·11·11·1···1·1111···11111······1···1····11·11111··11111···1········1·1·11·····1···111·1·1·1··11···1·1·······111·1······111·111·11·11·1111··11·······111·1·1··1··111·1···111···1·1·1····1····1···········1··1·11··11···1··1·1··11··1··1·1111···11111·······1···1···11·11·111·11111··1········11·11·······1····111···1·1·1·11···1·
out 79 (171)···11·········111··1·1·1·11·····11·1····111·11111··1111··1····11··1···11·1···········1···1··1111··1·1111··11·1···1·11·11·1·11·1··111··1········11··1···11111·1··1·11·11··1·····1·11··1·11····1111········1·····111·········11·1··1·1·111·······111·····111···11·111···1·111·········11··1···111·········1···1·1·1·1··1···111·1··1·1··1·····1··1111·1·11·1··111··1····1····11·1···11·111···1·1111··1·····111··1·1·11·····1111·········1·····1
check 80 (198)····11··11··11·1··111111·111··11·····11111·1··11··11·1··11·11··111··1·11·1··1·1·1··1·1·111··1··11··1·11····1·111··1···1··1111····1·111·1···1···1··111··1·11·····1111··1·1·1···11·1·1··1··11·1·····1·111···1·1·11·11····1111·1···111111111··1··1····11·111··1····11···11··1··1·1·1····111···1111····11·11111·1·····1·1··1··11······1··1·11···1···1··1111····1·111·1····1···1·111··1··11····1111·1·1·1···111·1····1··111·········1·111··1·1·11
check 81 (198)····1·1·1····11·11·1·111··1··1111··111·1··11····111111··11111··11·1····1··1···111··1·1··1···11····11··1···1·····111···1···1··111·111·1·11·····11···1111···1···111·11····11·11·11·11·11·1····11·111·1111··11·1·1··1·1···1··11··11·1·111·1·1·1··11·111··1··1·1······1·111·11··111·1····11·1····1···1··11111·1···1······1·1···1····1·········111···1···1··111·111·1·11······11··1111····1··111·11···11·11·1111·1··1·1···1··1·11·1··1111·11·1·1·
check 82 (172)···11·11····11·1···1·11··11··1·1···11··11·1·1·11·1·1····11··1··1·········11·1·1········1·1··1111··1·1·1··1····11·1·1···1·111··11·1·1···111·1·1····11··1·11·1·1·11·1···1·····1·1··111··1111·····11···11····1·111·11·11····11·1····1·11·11·1····1··11···11·1···1··11··1·1·····1···1····1········1··1·11····1··1·1·1·1··1···1·1···1·······11··1··1··1·111··11·1·1···11·1·11····11··1·1·1·1··11·1··1·····1·1·111·1··1111······11·····11···1·111·
check 83 (144)·····1·11···1·1··111·11············1····11··1·1·111··1·11··11·1···111·11·1··1··1·······1·1···11········11··11···1·1······1···1·1··1······1·1·········1·1···1··1··1·1··········11·111·111·11··1·1111··1···1···1····1·1··1·1·1···111·11············1·····11····1··1·1·11···1·11·1·1···1···1·11111····1·1···1··1·1·1············11···11······1·1······1···1·1··1·······1·1········1·1····1·1··1·1·········11111···111·11···1·11·1·1··1··1···1··
check 84 (184)···1··1·····111··1···1·1·1·1··1·1···11·111··1·1·1·1111··1··11··1·11······11·1··1·······11·····111···11111··11·11·1·11·11·11111111·1······1·1·1····1·11·11······111····1·1·1··1·1···1·1·1·11·1·1··111·····1··1·111··1·····111···1···1·11·1··1···1··11··111····1··1·1··11·11··1·1·1····1·11·····1··1·1·1···11·····1·1·1····111·11···11···11··1··1111·11111111·1·······1·11····1·11·11······111···1·1·1··1·1··1···1·1·111···1···1·11····1··1·11
check 85 (182)····11·111···111·1·111·1···1·1·1·1···1·11··111··11·11·1·1·11···1····1·····1····1·······1·····1111······11·1111111··1··1··1····11···1111·1··1······111··111···111··1··11·111·11·····11·11111·····1·1·1·1·····11·1·11·1··11·111··1·111·1··11····1·1··1··11···1·11···1·1·1·1·1·111······1·····1·····1···1···1····1·1·1·1········11·1·11·1·11·1···1·1··1····11···1111·1···1·····111··11·1···11··1·11·111·11····111··11111······1···1·1·1····11·1
check 86 (184)···1·1···1···11····1·111·111···11···11······111·1·11111···1·1·1·11111·1··11·1··11··1····11·········1111··11·····11·1··11·11··111·1·1····1··1·1·11·111·1··1·····11·11····1··1·1·1·11····1111···1·1··1111···1····11·1·····1·11·····1·111111·····11··11·········11·1·1··11·111··1··1···1·111·111·1··1·1·111··1·1··········1·111···11·········11··1·11·11··111·1·1····1···11··11111·1···1····11·11···1··1·1·111······1111····1·1····1111··1····1
check 87 (176)···1111111··1··1·11······1···1··11··111··111·······11·111··1··1···11··1···1·1········1·1·1···1··1·11·1·1··1·1···11····11···1·1·1·11·11111······1·····1··1111··1··1·······1·1·1···111111·1·1··11111··111··1····1111111··111··1··11·····1··1·····11·111···11·1··········1·1·111·1·····1···1·1·1····1·1····11··1·1·····11·1··1··1··1··1······11····11···1·1·1·11·11111·······1····1··1·111·1··1······1·1·1··1111··11·1·1···1111·1···111·1····11
check 88 (172)···1··1·1···1·1111·11111··1···1··1··1··1··1··1·1·1111·1··11········1··11·1····11·····1·111··11111·1····11··1···11···1····1···1·111111···11···1·1······1··1·1·1·111·1····1·1·1··1·1·1·11··1···1·1··11········11111··1···1·1·11·11·11111·1···1····1·1···1··1····1··1··111·1·1··1············1·111·····11··111·1·1·1·1·11·······11···1·····1·1····1···1···1·111111···1·1··1··1·····1···1·1··111·1···1·1·1··11·1·1·11··1····1·1····11·······1111
check 89 (176)·····11·11····1····1·111·111···11······111···1··1··111·1···11·1··111··11·1··1·111······11··········11111·1···1·1····1·11·11··111·1·1····1··1····1·1·1·1·11·····11·11·······1···1··1·1··11·1·1·1111·1111··1··11·1··11···11··1·····1·111111·····11······111·····1···1···1·11·1··1·1···1··11·1·111····1111··11············1·111·1·1·····1··1······111·11··111·1·1····1···1····11·1·1·1·1····11·11······1···1·1·1····11·11···111·1··1111·1··11·1
check 90 (182)···11·1··1······1·1·1·1··1·1·11··1··11·1····1·11···1·11···1····1·1111·11·11·1·11·····1··11···1111··11·11··1····1···1······11·1111·1··1··1·····11··11····1111·11·1111·11·1···1111···11·11111··1·11·····1·······1·11·1····1·····1·1·1·1·1·11·1····1·11··1······1··11····1··11··1·······1·11·11111··1·111··1·1·1·1·1·1·1··1·1·1·1··1·······1·····1·····11·1111·1··1··1······11·11····1·111·1·111111·1···1111··111··11111···1·11·······1······1·
check 91 (256)111·1····1111·11·1··1··111111·111111·1··11·1···11·111··1·11··11···1111··1··111··11111·1···111··1111·111·11····111··1·11111111··1·1·11··11·111···111·1··1111·11·1····1111·11·11··11····1·11111··1·11111·11·111·1·1·111111··1··11·11·11····11·11····1·111··11·11111··11··1·11·1·111111·111·1··1111111·11··1111111111·1··111···11··1111111··1·111·1··1····11·1·1··11··111·1111··1·11··1··111·1111··11··1··11·111111·1····1111·11·1····111·1·1·1
check 92 (206)·1····1··1·1···11····11111··111·11··111·1··11·1··111·1·1·····11·1111····1··1·11111·1···11··11······11····1111·11·1····11·····11·11··1··1···1·11·····1·111····11··11·1·1·11111··1··1111·11·11·11·····1··1·111·1111·111·1···1·····1·11·111·1111·11·11·11···1·····111·11·11······1·1·1·111·11111··1·1··1·1·1·11·11·1·1·11·····1·1··111··1··11···1·1·111·1··111··111···1·1·····11····1··1·1···11····11·1·11··11·11····111·1··11·1·1·111·11····1·
check 93 (220)··11·1···1·····1·1··1··11·1111·1·1·1·1··111·1··1·1·11···11····1····111···1111·1·1·11··1·11···111·11·11·11··1····1····11·11111··11111···11111·111·11111·1·1··1····1··1··111···1····1·1··1·1··1··1··1···1·11·1··1···111··1·11·1111·1·····1·1·11·11·11···1·1111·111·1111··11·11111··11··1··11111··1·111·11··11··1··11······1·1·1·1·111·11··111·11······11·1·1··1111·1·11··11·1··11·11·1·····111·1··11111·111··11111·11···1··1···111·11111·1···1
check 94 (212)···1······11·1·1·11··11···111·111···11111111··1·1·1····11·1··1111··1·1·····1···11111·····1··1·111·1·11·1111·1···11···1·1··1·1·111111·1··1·11···1·111·1111·1··11···1··1·1·····1···1··1·11···1···1111111111·1·1··111111····1··1····1111·1····1·1··1·11·1··11·111111·1·1·11···1··1····1··1····11···111··1····11·1·1·1··11111·1··1···1·1··111111··1111···1·11111··1···1·11·····1·1·11··111·1·11·1··11····1·111····1111··111···1·1·11111·1·1··11·
check 95 (220)···1·1··1·11·1·1·1····111···11·1111····1·1111···11111··1·11··1·1···1··1·11111·1·····1111····11··11···111·1···1·11··1···111···1·1···111·1··1···1·1·····1··1·1·111···111·111··1··11·1··1·11·····11··1111····1111111·1··11·11··1··1···1··1111····11111111·111·1·1··11·1···11··1·1·111111·····1·11·11·111·····11111····1·1111111·1·1··111·11·11···1···1·111··1···1111·11111··1·1·111·111··1·11·11··1111··1··11·11·1··11····11··11111111··1·1····
check 96 (216)···1··11·1······111··11·1··11·1·····1··11111··111····1·11·11··1·1·11·1111··1·······1·1·11·1111·111·1·11·1···11·1···1·1111···1·11111·11·11··111··1111··1··11·······1·····1·1111··1·11··11·11·1··111111··11··1·1·11··11···1··111···11··111···1······1···11··1·1111···11111·1·1111·····1··1·1·1··11111····1111····111·1·11·1111··1····1·1··1·1111·1··1111·111111·11·11···1·111···11·111·1······1·····1····111··111111·111····11·1····1111111·1·
check 97 (214)···1·····1··11111·11··1··11···11·111·11·1111···1·1·1·1·11······111··1·····1··1·1111·11111·1111·1·11·1··11·1··1111··1··1··111····1·1111··1·111··1111111··11·1·1·1······1·1··11·11·1·1···1·1·1·····11·1·1111·1111·1·······11111·1·11··1·11·11·11·1··1··11···1·11111·11·1·1·1·11········111···1·····1·11··1···111·111·11·111····11·1····1·11·1···1·1··111··11·1····11·111·111······11·1··1··1·····1·1··11·111·1·1··1·1·111111111·1·1·1·1·11···1
check 98 (216)···11···1···1·1··111··1···1··1·111···11··111·1·1···1·111111·11····11·11111·1·111·111111·1·111··1111·1·11·11·11·····11······1·11··111··11········1·11·1·1·1··11·····11·111·1·1··11·1····11·11··11····11·111·11·1·11·····1·1·1···111··1··1·1····111··11···11·1··1··1····1·1·····11·1111111·1·1···11111··1··1·1111111·1··111··1·1·11··1·1········11·····1·11··111··11·········111·1·1··111111111·1·1·1·1·11·1·111111··1·1111··111111··11·11·1·1
check 99 (196)·····1·1····111··11·1·1··1···1·111·1···1··········11·111·1··1··11·11··11·1······1··1········1·1···1·1111··11111····1111·11·1·1·1·1·····1111·1····1·1····1·1·1··111··1·11··1·1·1111·11111·1111·1·1·1·1··111·1··11··1·1····111···11·1·1·1··1····1111····1··············11··111····1····11·1·1·111·······11········1····1···1··1·11·1··1·1·111111···11·1·1·1·1·11111··1·11111111·1111·11·111···111·111·1·1···1···1···1···111·1·111·1·111·1111··

The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.

Figures of merit

inputs n428Noisy T states per run.
outputs k80
distance d4Exact, proved and witnessed here.
error coefficient A_{4}7,936Faults of weight 4 in the circuit shown that pass every check and damage the output. The output error is A_{4}\,p^{4} to leading order.
wires N100
checks r20
V_{\mathrm{ex}}80T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.2098Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.2098Overhead per output qubit.
\gamma_T = \log(n/T)/\log dnot computedOverhead per unit of T-count.
T-countnot computedMinimal T-count of the output gate. Not computable at this width.
phase-polynomial degreenot computedMinimised over changes of output basis.
effective width80Rank of the output rows modulo the check rows.

Output gate

80 T0 CS0 CCZon 80 output wires

As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}\cdot \mathrm{T}_{71}\cdot \mathrm{T}_{72}\cdot \mathrm{T}_{73}\cdot \mathrm{T}_{74}\cdot \mathrm{T}_{75}\cdot \mathrm{T}_{76}\cdot \mathrm{T}_{77}\cdot \mathrm{T}_{78}\cdot \mathrm{T}_{79}

As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79 (output wires per term, separated by +)

This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.

Clifford correction

With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 92 single-wire gates and 1407 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S}^\dagger on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{S}^\dagger on output 6, \mathrm{S}^\dagger on output 7, \mathrm{Z} on output 8, \mathrm{Z} on output 9, \mathrm{S}^\dagger on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{Z} on output 14, \mathrm{S}^\dagger on output 15, \mathrm{S} on output 16, \mathrm{S}^\dagger on output 17, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{S} on output 22, \mathrm{S}^\dagger on output 23 and 1475 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

All 1499 correction gates

\mathrm{Z} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S}^\dagger on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{S}^\dagger on output 6, \mathrm{S}^\dagger on output 7, \mathrm{Z} on output 8, \mathrm{Z} on output 9, \mathrm{S}^\dagger on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{Z} on output 14, \mathrm{S}^\dagger on output 15, \mathrm{S} on output 16, \mathrm{S}^\dagger on output 17, \mathrm{Z} on output 18, \mathrm{Z} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{S} on output 22, \mathrm{S}^\dagger on output 23, \mathrm{Z} on output 24, \mathrm{Z} on output 25, \mathrm{S} on output 26, \mathrm{S}^\dagger on output 27, \mathrm{Z} on output 28, \mathrm{S} on output 29, \mathrm{S} on output 30, \mathrm{S} on output 31, \mathrm{S} on output 32, \mathrm{S} on output 33, \mathrm{Z} on output 34, \mathrm{Z} on output 35, \mathrm{S} on output 36, \mathrm{Z} on output 37, \mathrm{Z} on output 38, \mathrm{S} on output 39, \mathrm{S} on output 40, \mathrm{Z} on output 41, \mathrm{Z} on output 42, \mathrm{S}^\dagger on output 43, \mathrm{S} on output 44, \mathrm{S} on output 45, \mathrm{S} on output 46, \mathrm{S}^\dagger on output 47, \mathrm{Z} on output 48, \mathrm{S} on output 49, \mathrm{Z} on output 50, \mathrm{Z} on output 51, \mathrm{Z} on output 52, \mathrm{S}^\dagger on output 53, \mathrm{S} on output 54, \mathrm{S}^\dagger on output 55, \mathrm{S}^\dagger on output 56, \mathrm{Z} on output 57, \mathrm{S} on output 58, \mathrm{Z} on output 59, \mathrm{S}^\dagger on output 60, \mathrm{Z} on output 61, \mathrm{S}^\dagger on output 62, \mathrm{S} on output 63, \mathrm{S}^\dagger on output 64, \mathrm{S} on output 65, \mathrm{S}^\dagger on output 66, \mathrm{S} on output 67, \mathrm{Z} on output 68, \mathrm{Z} on output 69, \mathrm{S}^\dagger on output 70, \mathrm{S} on output 71, \mathrm{S} on output 72, \mathrm{S}^\dagger on output 73, \mathrm{S}^\dagger on output 74, \mathrm{S}^\dagger on output 75, \mathrm{S} on output 76, \mathrm{Z} on output 77, \mathrm{Z} on output 78, \mathrm{S}^\dagger on output 79, \mathrm{S} on check 80, \mathrm{S} on check 81, \mathrm{Z} on check 82, \mathrm{S} on check 85, \mathrm{Z} on check 88, \mathrm{S} on check 90, \mathrm{S} on check 92, \mathrm{Z} on check 93, \mathrm{Z} on check 94, \mathrm{Z} on check 95, \mathrm{S} on check 97, \mathrm{Z} on check 99, \mathrm{CZ} on output 0, output 2, \mathrm{CZ} on output 0, output 3, \mathrm{CZ} on output 0, output 6, \mathrm{CZ} on output 0, output 7, \mathrm{CZ} on output 0, output 8, \mathrm{CZ} on output 0, output 10, \mathrm{CZ} on output 0, output 15, \mathrm{CZ} on output 0, output 17, \mathrm{CZ} on output 0, output 18, \mathrm{CZ} on output 0, output 23, \mathrm{CZ} on output 0, output 25, \mathrm{CZ} on output 0, output 27, \mathrm{CZ} on output 0, output 28, \mathrm{CZ} on output 0, output 34, \mathrm{CZ} on output 0, output 37, \mathrm{CZ} on output 0, output 38, \mathrm{CZ} on output 0, output 41, \mathrm{CZ} on output 0, output 43, \mathrm{CZ} on output 0, output 47, \mathrm{CZ} on output 0, output 48, \mathrm{CZ} on output 0, output 50, \mathrm{CZ} on output 0, output 53, \mathrm{CZ} on output 0, output 55, \mathrm{CZ} on output 0, output 56, \mathrm{CZ} on output 0, output 57, \mathrm{CZ} on output 0, output 59, \mathrm{CZ} on output 0, output 60, \mathrm{CZ} on output 0, output 62, \mathrm{CZ} on output 0, output 64, \mathrm{CZ} on output 0, output 66, \mathrm{CZ} on output 0, output 68, \mathrm{CZ} on output 0, output 70, \mathrm{CZ} on output 0, output 73, \mathrm{CZ} on output 0, output 74, \mathrm{CZ} on output 0, output 75, \mathrm{CZ} on output 0, output 79, \mathrm{CZ} on output 0, check 82, \mathrm{CZ} on output 0, check 85, \mathrm{CZ} on output 0, check 88, \mathrm{CZ} on output 0, check 90, \mathrm{CZ} on output 0, check 93, \mathrm{CZ} on output 0, check 94, \mathrm{CZ} on output 0, check 95, \mathrm{CZ} on output 0, check 97, \mathrm{CZ} on output 0, check 99, \mathrm{CZ} on output 2, output 3, \mathrm{CZ} on output 2, output 6, \mathrm{CZ} on output 2, output 7, \mathrm{CZ} on output 2, output 8, \mathrm{CZ} on output 2, output 10, \mathrm{CZ} on output 2, output 15, \mathrm{CZ} on output 2, output 17, \mathrm{CZ} on output 2, output 18, \mathrm{CZ} on output 2, output 23, \mathrm{CZ} on output 2, output 25, \mathrm{CZ} on output 2, output 27, \mathrm{CZ} on output 2, output 28, \mathrm{CZ} on output 2, output 34, \mathrm{CZ} on output 2, output 37, \mathrm{CZ} on output 2, output 38, \mathrm{CZ} on output 2, output 41, \mathrm{CZ} on output 2, output 43, \mathrm{CZ} on output 2, output 47, \mathrm{CZ} on output 2, output 48, \mathrm{CZ} on output 2, output 50, \mathrm{CZ} on output 2, output 53, \mathrm{CZ} on output 2, output 55, \mathrm{CZ} on output 2, output 56, \mathrm{CZ} on output 2, output 57, \mathrm{CZ} on output 2, output 59, \mathrm{CZ} on output 2, output 60, \mathrm{CZ} on output 2, output 62, \mathrm{CZ} on output 2, output 64, \mathrm{CZ} on output 2, output 66, \mathrm{CZ} on output 2, output 68, \mathrm{CZ} on output 2, output 70, \mathrm{CZ} on output 2, output 73, \mathrm{CZ} on output 2, output 74, \mathrm{CZ} on output 2, output 75, \mathrm{CZ} on output 2, output 79, \mathrm{CZ} on output 2, check 82, \mathrm{CZ} on output 2, check 85, \mathrm{CZ} on output 2, check 88, \mathrm{CZ} on output 2, check 90, \mathrm{CZ} on output 2, check 93, \mathrm{CZ} on output 2, check 94, \mathrm{CZ} on output 2, check 95, \mathrm{CZ} on output 2, check 97, \mathrm{CZ} on output 2, check 99, \mathrm{CZ} on output 3, output 4, \mathrm{CZ} on output 3, output 8, \mathrm{CZ} on output 3, output 9, \mathrm{CZ} on output 3, output 11, \mathrm{CZ} on output 3, output 12, \mathrm{CZ} on output 3, output 14, \mathrm{CZ} on output 3, output 18, \mathrm{CZ} on output 3, output 19, \mathrm{CZ} on output 3, output 20, \mathrm{CZ} on output 3, output 21, \mathrm{CZ} on output 3, output 24, \mathrm{CZ} on output 3, output 25, \mathrm{CZ} on output 3, output 28, \mathrm{CZ} on output 3, output 34, \mathrm{CZ} on output 3, output 35, \mathrm{CZ} on output 3, output 37, \mathrm{CZ} on output 3, output 38, \mathrm{CZ} on output 3, output 41, \mathrm{CZ} on output 3, output 42, \mathrm{CZ} on output 3, output 48, \mathrm{CZ} on output 3, output 50, \mathrm{CZ} on output 3, output 51, \mathrm{CZ} on output 3, output 52, \mathrm{CZ} on output 3, output 57, \mathrm{CZ} on output 3, output 59, \mathrm{CZ} on output 3, output 61, \mathrm{CZ} on output 3, output 68, \mathrm{CZ} on output 3, output 69, \mathrm{CZ} on output 3, output 77, \mathrm{CZ} on output 3, output 78, \mathrm{CZ} on output 3, check 80, \mathrm{CZ} on output 3, check 81, \mathrm{CZ} on output 3, check 85, \mathrm{CZ} on output 3, check 90, \mathrm{CZ} on output 3, check 92, \mathrm{CZ} on output 3, check 97, \mathrm{CZ} on output 4, output 6, \mathrm{CZ} on output 4, output 7, \mathrm{CZ} on output 4, output 9, \mathrm{CZ} on output 4, output 10, \mathrm{CZ} on output 4, output 11, \mathrm{CZ} on output 4, output 12, \mathrm{CZ} on output 4, output 14, \mathrm{CZ} on output 4, output 15, \mathrm{CZ} on output 4, output 17, \mathrm{CZ} on output 4, output 19, \mathrm{CZ} on output 4, output 20, \mathrm{CZ} on output 4, output 21, \mathrm{CZ} on output 4, output 23, \mathrm{CZ} on output 4, output 24, \mathrm{CZ} on output 4, output 27, \mathrm{CZ} on output 4, output 35, \mathrm{CZ} on output 4, output 42, \mathrm{CZ} on output 4, output 43, \mathrm{CZ} on output 4, output 47, \mathrm{CZ} on output 4, output 51, \mathrm{CZ} on output 4, output 52, \mathrm{CZ} on output 4, output 53, \mathrm{CZ} on output 4, output 55, \mathrm{CZ} on output 4, output 56, \mathrm{CZ} on output 4, output 60, \mathrm{CZ} on output 4, output 61, \mathrm{CZ} on output 4, output 62, \mathrm{CZ} on output 4, output 64, \mathrm{CZ} on output 4, output 66, \mathrm{CZ} on output 4, output 69, \mathrm{CZ} on output 4, output 70, \mathrm{CZ} on output 4, output 73, \mathrm{CZ} on output 4, output 74, \mathrm{CZ} on output 4, output 75, \mathrm{CZ} on output 4, output 77, \mathrm{CZ} on output 4, output 78, \mathrm{CZ} on output 4, output 79, \mathrm{CZ} on output 4, check 80, \mathrm{CZ} on output 4, check 81, \mathrm{CZ} on output 4, check 82, \mathrm{CZ} on output 4, check 88, \mathrm{CZ} on output 4, check 92, \mathrm{CZ} on output 4, check 93, \mathrm{CZ} on output 4, check 94, \mathrm{CZ} on output 4, check 95, \mathrm{CZ} on output 4, check 99, \mathrm{CZ} on output 6, output 8, \mathrm{CZ} on output 6, output 9, \mathrm{CZ} on output 6, output 11, \mathrm{CZ} on output 6, output 12, \mathrm{CZ} on output 6, output 14, \mathrm{CZ} on output 6, output 18, \mathrm{CZ} on output 6, output 19, \mathrm{CZ} on output 6, output 20, \mathrm{CZ} on output 6, output 21, \mathrm{CZ} on output 6, output 24, \mathrm{CZ} on output 6, output 25, \mathrm{CZ} on output 6, output 28, \mathrm{CZ} on output 6, output 34, \mathrm{CZ} on output 6, output 35, \mathrm{CZ} on output 6, output 37, \mathrm{CZ} on output 6, output 38, \mathrm{CZ} on output 6, output 41, \mathrm{CZ} on output 6, output 42, \mathrm{CZ} on output 6, output 48, \mathrm{CZ} on output 6, output 50, \mathrm{CZ} on output 6, output 51, \mathrm{CZ} on output 6, output 52, \mathrm{CZ} on output 6, output 57, \mathrm{CZ} on output 6, output 59, \mathrm{CZ} on output 6, output 61, \mathrm{CZ} on output 6, output 68, \mathrm{CZ} on output 6, output 69, \mathrm{CZ} on output 6, output 77, \mathrm{CZ} on output 6, output 78, \mathrm{CZ} on output 6, check 80, \mathrm{CZ} on output 6, check 81, \mathrm{CZ} on output 6, check 85, \mathrm{CZ} on output 6, check 90, \mathrm{CZ} on output 6, check 92, \mathrm{CZ} on output 6, check 97, \mathrm{CZ} on output 7, output 8, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, output 11, \mathrm{CZ} on output 7, output 12, \mathrm{CZ} on output 7, output 14, \mathrm{CZ} on output 7, output 18, \mathrm{CZ} on output 7, output 19, \mathrm{CZ} on output 7, output 20, \mathrm{CZ} on output 7, output 21, \mathrm{CZ} on output 7, output 24, \mathrm{CZ} on output 7, output 25, \mathrm{CZ} on output 7, output 28, \mathrm{CZ} on output 7, output 34, \mathrm{CZ} on output 7, output 35, \mathrm{CZ} on output 7, output 37, \mathrm{CZ} on output 7, output 38, \mathrm{CZ} on output 7, output 41, \mathrm{CZ} on output 7, output 42, \mathrm{CZ} on output 7, output 48, \mathrm{CZ} on output 7, output 50, \mathrm{CZ} on output 7, output 51, \mathrm{CZ} on output 7, output 52, \mathrm{CZ} on output 7, output 57, \mathrm{CZ} on output 7, output 59, \mathrm{CZ} on output 7, output 61, \mathrm{CZ} on output 7, output 68, \mathrm{CZ} on output 7, output 69, \mathrm{CZ} on output 7, output 77, \mathrm{CZ} on output 7, output 78, \mathrm{CZ} on output 7, check 80, \mathrm{CZ} on output 7, check 81, \mathrm{CZ} on output 7, check 85, \mathrm{CZ} on output 7, check 90, \mathrm{CZ} on output 7, check 92, \mathrm{CZ} on output 7, check 97, \mathrm{CZ} on output 8, output 10, \mathrm{CZ} on output 8, output 15, \mathrm{CZ} on output 8, output 17, \mathrm{CZ} on output 8, output 18, \mathrm{CZ} on output 8, output 23, \mathrm{CZ} on output 8, output 25, \mathrm{CZ} on output 8, output 27, \mathrm{CZ} on output 8, output 28, \mathrm{CZ} on output 8, output 34, \mathrm{CZ} on output 8, output 37, \mathrm{CZ} on output 8, output 38, \mathrm{CZ} on output 8, output 41, \mathrm{CZ} on output 8, output 43, \mathrm{CZ} on output 8, output 47, \mathrm{CZ} on output 8, output 48, \mathrm{CZ} on output 8, output 50, \mathrm{CZ} on output 8, output 53, \mathrm{CZ} on output 8, output 55, \mathrm{CZ} on output 8, output 56, \mathrm{CZ} on output 8, output 57, \mathrm{CZ} on output 8, output 59, \mathrm{CZ} on output 8, output 60, \mathrm{CZ} on output 8, output 62, \mathrm{CZ} on output 8, output 64, \mathrm{CZ} on output 8, output 66, \mathrm{CZ} on output 8, output 68, \mathrm{CZ} on output 8, output 70, \mathrm{CZ} on output 8, output 73, \mathrm{CZ} on output 8, output 74, \mathrm{CZ} on output 8, output 75, \mathrm{CZ} on output 8, output 79, \mathrm{CZ} on output 8, check 82, \mathrm{CZ} on output 8, check 85, \mathrm{CZ} on output 8, check 88, \mathrm{CZ} on output 8, check 90, \mathrm{CZ} on output 8, check 93, \mathrm{CZ} on output 8, check 94, \mathrm{CZ} on output 8, check 95, \mathrm{CZ} on output 8, check 97, \mathrm{CZ} on output 8, check 99, \mathrm{CZ} on output 9, output 10, \mathrm{CZ} on output 9, output 11, \mathrm{CZ} on output 9, output 12, \mathrm{CZ} on output 9, output 14, \mathrm{CZ} on output 9, output 15, \mathrm{CZ} on output 9, output 17, \mathrm{CZ} on output 9, output 19, \mathrm{CZ} on output 9, output 20, \mathrm{CZ} on output 9, output 21, \mathrm{CZ} on output 9, output 23, \mathrm{CZ} on output 9, output 24, \mathrm{CZ} on output 9, output 27, \mathrm{CZ} on output 9, output 35, \mathrm{CZ} on output 9, output 42, \mathrm{CZ} on output 9, output 43, \mathrm{CZ} on output 9, output 47, \mathrm{CZ} on output 9, output 51, \mathrm{CZ} on output 9, output 52, \mathrm{CZ} on output 9, output 53, \mathrm{CZ} on output 9, output 55, \mathrm{CZ} on output 9, output 56, \mathrm{CZ} on output 9, output 60, \mathrm{CZ} on output 9, output 61, \mathrm{CZ} on output 9, output 62, \mathrm{CZ} on output 9, output 64, \mathrm{CZ} on output 9, output 66, \mathrm{CZ} on output 9, output 69, \mathrm{CZ} on output 9, output 70, \mathrm{CZ} on output 9, output 73, \mathrm{CZ} on output 9, output 74, \mathrm{CZ} on output 9, output 75, \mathrm{CZ} on output 9, output 77, \mathrm{CZ} on output 9, output 78, \mathrm{CZ} on output 9, output 79, \mathrm{CZ} on output 9, check 80, \mathrm{CZ} on output 9, check 81, \mathrm{CZ} on output 9, check 82, \mathrm{CZ} on output 9, check 88, \mathrm{CZ} on output 9, check 92, \mathrm{CZ} on output 9, check 93, \mathrm{CZ} on output 9, check 94, \mathrm{CZ} on output 9, check 95, \mathrm{CZ} on output 9, check 99, \mathrm{CZ} on output 10, output 11, \mathrm{CZ} on output 10, output 12, \mathrm{CZ} on output 10, output 14, \mathrm{CZ} on output 10, output 18, \mathrm{CZ} on output 10, output 19, \mathrm{CZ} on output 10, output 20, \mathrm{CZ} on output 10, output 21, \mathrm{CZ} on output 10, output 24, \mathrm{CZ} on output 10, output 25, \mathrm{CZ} on output 10, output 28, \mathrm{CZ} on output 10, output 34, \mathrm{CZ} on output 10, output 35, \mathrm{CZ} on output 10, output 37, \mathrm{CZ} on output 10, output 38, \mathrm{CZ} on output 10, output 41, \mathrm{CZ} on output 10, output 42, \mathrm{CZ} on output 10, output 48, \mathrm{CZ} on output 10, output 50, \mathrm{CZ} on output 10, output 51, \mathrm{CZ} on output 10, output 52, \mathrm{CZ} on output 10, output 57, \mathrm{CZ} on output 10, output 59, \mathrm{CZ} on output 10, output 61, \mathrm{CZ} on output 10, output 68, \mathrm{CZ} on output 10, output 69, \mathrm{CZ} on output 10, output 77, \mathrm{CZ} on output 10, output 78, \mathrm{CZ} on output 10, check 80, \mathrm{CZ} on output 10, check 81, \mathrm{CZ} on output 10, check 85, \mathrm{CZ} on output 10, check 90, \mathrm{CZ} on output 10, check 92, \mathrm{CZ} on output 10, check 97, \mathrm{CZ} on output 11, output 12, \mathrm{CZ} on output 11, output 14, \mathrm{CZ} on output 11, output 15, \mathrm{CZ} on output 11, output 17, \mathrm{CZ} on output 11, output 19, \mathrm{CZ} on output 11, output 20, \mathrm{CZ} on output 11, output 21, \mathrm{CZ} on output 11, output 23, \mathrm{CZ} on output 11, output 24, \mathrm{CZ} on output 11, output 27, \mathrm{CZ} on output 11, output 35, \mathrm{CZ} on output 11, output 42, \mathrm{CZ} on output 11, output 43, \mathrm{CZ} on output 11, output 47, \mathrm{CZ} on output 11, output 51, \mathrm{CZ} on output 11, output 52, \mathrm{CZ} on output 11, output 53, \mathrm{CZ} on output 11, output 55, \mathrm{CZ} on output 11, output 56, \mathrm{CZ} on output 11, output 60, \mathrm{CZ} on output 11, output 61, \mathrm{CZ} on output 11, output 62, \mathrm{CZ} on output 11, output 64, \mathrm{CZ} on output 11, output 66, \mathrm{CZ} on output 11, output 69, \mathrm{CZ} on output 11, output 70, \mathrm{CZ} on output 11, output 73, \mathrm{CZ} on output 11, output 74, \mathrm{CZ} on output 11, output 75, \mathrm{CZ} on output 11, output 77, \mathrm{CZ} on output 11, output 78, \mathrm{CZ} on output 11, output 79, \mathrm{CZ} on output 11, check 80, \mathrm{CZ} on output 11, check 81, \mathrm{CZ} on output 11, check 82, \mathrm{CZ} on output 11, check 88, \mathrm{CZ} on output 11, check 92, \mathrm{CZ} on output 11, check 93, \mathrm{CZ} on output 11, check 94, \mathrm{CZ} on output 11, check 95, \mathrm{CZ} on output 11, check 99, \mathrm{CZ} on output 12, output 14, \mathrm{CZ} on output 12, output 15, \mathrm{CZ} on output 12, output 17, \mathrm{CZ} on output 12, output 19, \mathrm{CZ} on output 12, output 20, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, output 23, \mathrm{CZ} on output 12, output 24, \mathrm{CZ} on output 12, output 27, \mathrm{CZ} on output 12, output 35, \mathrm{CZ} on output 12, output 42, \mathrm{CZ} on output 12, output 43, \mathrm{CZ} on output 12, output 47, \mathrm{CZ} on output 12, output 51, \mathrm{CZ} on output 12, output 52, \mathrm{CZ} on output 12, output 53, \mathrm{CZ} on output 12, output 55, \mathrm{CZ} on output 12, output 56, \mathrm{CZ} on output 12, output 60, \mathrm{CZ} on output 12, output 61, \mathrm{CZ} on output 12, output 62, \mathrm{CZ} on output 12, output 64, \mathrm{CZ} on output 12, output 66, \mathrm{CZ} on output 12, output 69, \mathrm{CZ} on output 12, output 70, \mathrm{CZ} on output 12, output 73, \mathrm{CZ} on output 12, output 74, \mathrm{CZ} on output 12, output 75, \mathrm{CZ} on output 12, output 77, \mathrm{CZ} on output 12, output 78, \mathrm{CZ} on output 12, output 79, \mathrm{CZ} on output 12, check 80, \mathrm{CZ} on output 12, check 81, \mathrm{CZ} on output 12, check 82, \mathrm{CZ} on output 12, check 88, \mathrm{CZ} on output 12, check 92, \mathrm{CZ} on output 12, check 93, \mathrm{CZ} on output 12, check 94, \mathrm{CZ} on output 12, check 95, \mathrm{CZ} on output 12, check 99, \mathrm{CZ} on output 14, output 15, \mathrm{CZ} on output 14, output 17, \mathrm{CZ} on output 14, output 19, \mathrm{CZ} on output 14, output 20, \mathrm{CZ} on output 14, output 21, \mathrm{CZ} on output 14, output 23, \mathrm{CZ} on output 14, output 24, \mathrm{CZ} on output 14, output 27, \mathrm{CZ} on output 14, output 35, \mathrm{CZ} on output 14, output 42, \mathrm{CZ} on output 14, output 43, \mathrm{CZ} on output 14, output 47, \mathrm{CZ} on output 14, output 51, \mathrm{CZ} on output 14, output 52, \mathrm{CZ} on output 14, output 53, \mathrm{CZ} on output 14, output 55, \mathrm{CZ} on output 14, output 56, \mathrm{CZ} on output 14, output 60, \mathrm{CZ} on output 14, output 61, \mathrm{CZ} on output 14, output 62, \mathrm{CZ} on output 14, output 64, \mathrm{CZ} on output 14, output 66, \mathrm{CZ} on output 14, output 69, \mathrm{CZ} on output 14, output 70, \mathrm{CZ} on output 14, output 73, \mathrm{CZ} on output 14, output 74, \mathrm{CZ} on output 14, output 75, \mathrm{CZ} on output 14, output 77, \mathrm{CZ} on output 14, output 78, \mathrm{CZ} on output 14, output 79, \mathrm{CZ} on output 14, check 80, \mathrm{CZ} on output 14, check 81, \mathrm{CZ} on output 14, check 82, \mathrm{CZ} on output 14, check 88, \mathrm{CZ} on output 14, check 92, \mathrm{CZ} on output 14, check 93, \mathrm{CZ} on output 14, check 94, \mathrm{CZ} on output 14, check 95, \mathrm{CZ} on output 14, check 99, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 19, \mathrm{CZ} on output 15, output 20, \mathrm{CZ} on output 15, output 21, \mathrm{CZ} on output 15, output 24, \mathrm{CZ} on output 15, output 25, \mathrm{CZ} on output 15, output 28, \mathrm{CZ} on output 15, output 34, \mathrm{CZ} on output 15, output 35, \mathrm{CZ} on output 15, output 37, \mathrm{CZ} on output 15, output 38, \mathrm{CZ} on output 15, output 41, \mathrm{CZ} on output 15, output 42, \mathrm{CZ} on output 15, output 48, \mathrm{CZ} on output 15, output 50, \mathrm{CZ} on output 15, output 51, \mathrm{CZ} on output 15, output 52, \mathrm{CZ} on output 15, output 57, \mathrm{CZ} on output 15, output 59, \mathrm{CZ} on output 15, output 61, \mathrm{CZ} on output 15, output 68, \mathrm{CZ} on output 15, output 69, \mathrm{CZ} on output 15, output 77, \mathrm{CZ} on output 15, output 78, \mathrm{CZ} on output 15, check 80, \mathrm{CZ} on output 15, check 81, \mathrm{CZ} on output 15, check 85, \mathrm{CZ} on output 15, check 90, \mathrm{CZ} on output 15, check 92, \mathrm{CZ} on output 15, check 97, \mathrm{CZ} on output 17, output 18, \mathrm{CZ} on output 17, output 19, \mathrm{CZ} on output 17, output 20, \mathrm{CZ} on output 17, output 21, \mathrm{CZ} on output 17, output 24, \mathrm{CZ} on output 17, output 25, \mathrm{CZ} on output 17, output 28, \mathrm{CZ} on output 17, output 34, \mathrm{CZ} on output 17, output 35, \mathrm{CZ} on output 17, output 37, \mathrm{CZ} on output 17, output 38, \mathrm{CZ} on output 17, output 41, \mathrm{CZ} on output 17, output 42, \mathrm{CZ} on output 17, output 48, \mathrm{CZ} on output 17, output 50, \mathrm{CZ} on output 17, output 51, \mathrm{CZ} on output 17, output 52, \mathrm{CZ} on output 17, output 57, \mathrm{CZ} on output 17, output 59, \mathrm{CZ} on output 17, output 61, \mathrm{CZ} on output 17, output 68, \mathrm{CZ} on output 17, output 69, \mathrm{CZ} on output 17, output 77, \mathrm{CZ} on output 17, output 78, \mathrm{CZ} on output 17, check 80, \mathrm{CZ} on output 17, check 81, \mathrm{CZ} on output 17, check 85, \mathrm{CZ} on output 17, check 90, \mathrm{CZ} on output 17, check 92, \mathrm{CZ} on output 17, check 97, \mathrm{CZ} on output 18, output 23, \mathrm{CZ} on output 18, output 25, \mathrm{CZ} on output 18, output 27, \mathrm{CZ} on output 18, output 28, \mathrm{CZ} on output 18, output 34, \mathrm{CZ} on output 18, output 37, \mathrm{CZ} on output 18, output 38, \mathrm{CZ} on output 18, output 41, \mathrm{CZ} on output 18, output 43, \mathrm{CZ} on output 18, output 47, \mathrm{CZ} on output 18, output 48, \mathrm{CZ} on output 18, output 50, \mathrm{CZ} on output 18, output 53, \mathrm{CZ} on output 18, output 55, \mathrm{CZ} on output 18, output 56, \mathrm{CZ} on output 18, output 57, \mathrm{CZ} on output 18, output 59, \mathrm{CZ} on output 18, output 60, \mathrm{CZ} on output 18, output 62, \mathrm{CZ} on output 18, output 64, \mathrm{CZ} on output 18, output 66, \mathrm{CZ} on output 18, output 68, \mathrm{CZ} on output 18, output 70, \mathrm{CZ} on output 18, output 73, \mathrm{CZ} on output 18, output 74, \mathrm{CZ} on output 18, output 75, \mathrm{CZ} on output 18, output 79, \mathrm{CZ} on output 18, check 82, \mathrm{CZ} on output 18, check 85, \mathrm{CZ} on output 18, check 88, \mathrm{CZ} on output 18, check 90, \mathrm{CZ} on output 18, check 93, \mathrm{CZ} on output 18, check 94, \mathrm{CZ} on output 18, check 95, \mathrm{CZ} on output 18, check 97, \mathrm{CZ} on output 18, check 99, \mathrm{CZ} on output 19, output 20, \mathrm{CZ} on output 19, output 21, \mathrm{CZ} on output 19, output 23, \mathrm{CZ} on output 19, output 24, \mathrm{CZ} on output 19, output 27, \mathrm{CZ} on output 19, output 35, \mathrm{CZ} on output 19, output 42, \mathrm{CZ} on output 19, output 43, \mathrm{CZ} on output 19, output 47, \mathrm{CZ} on output 19, output 51, \mathrm{CZ} on output 19, output 52, \mathrm{CZ} on output 19, output 53, \mathrm{CZ} on output 19, output 55, \mathrm{CZ} on output 19, output 56, \mathrm{CZ} on output 19, output 60, \mathrm{CZ} on output 19, output 61, \mathrm{CZ} on output 19, output 62, \mathrm{CZ} on output 19, output 64, \mathrm{CZ} on output 19, output 66, \mathrm{CZ} on output 19, output 69, \mathrm{CZ} on output 19, output 70, \mathrm{CZ} on output 19, output 73, \mathrm{CZ} on output 19, output 74, \mathrm{CZ} on output 19, output 75, \mathrm{CZ} on output 19, output 77, \mathrm{CZ} on output 19, output 78, \mathrm{CZ} on output 19, output 79, \mathrm{CZ} on output 19, check 80, \mathrm{CZ} on output 19, check 81, \mathrm{CZ} on output 19, check 82, \mathrm{CZ} on output 19, check 88, \mathrm{CZ} on output 19, check 92, \mathrm{CZ} on output 19, check 93, \mathrm{CZ} on output 19, check 94, \mathrm{CZ} on output 19, check 95, \mathrm{CZ} on output 19, check 99, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, output 23, \mathrm{CZ} on output 20, output 24, \mathrm{CZ} on output 20, output 27, \mathrm{CZ} on output 20, output 35, \mathrm{CZ} on output 20, output 42, \mathrm{CZ} on output 20, output 43, \mathrm{CZ} on output 20, output 47, \mathrm{CZ} on output 20, output 51, \mathrm{CZ} on output 20, output 52, \mathrm{CZ} on output 20, output 53, \mathrm{CZ} on output 20, output 55, \mathrm{CZ} on output 20, output 56, \mathrm{CZ} on output 20, output 60, \mathrm{CZ} on output 20, output 61, \mathrm{CZ} on output 20, output 62, \mathrm{CZ} on output 20, output 64, \mathrm{CZ} on output 20, output 66, \mathrm{CZ} on output 20, output 69, \mathrm{CZ} on output 20, output 70, \mathrm{CZ} on output 20, output 73, \mathrm{CZ} on output 20, output 74, \mathrm{CZ} on output 20, output 75, \mathrm{CZ} on output 20, output 77, \mathrm{CZ} on output 20, output 78, \mathrm{CZ} on output 20, output 79, \mathrm{CZ} on output 20, check 80, \mathrm{CZ} on output 20, check 81, \mathrm{CZ} on output 20, check 82, \mathrm{CZ} on output 20, check 88, \mathrm{CZ} on output 20, check 92, \mathrm{CZ} on output 20, check 93, \mathrm{CZ} on output 20, check 94, \mathrm{CZ} on output 20, check 95, \mathrm{CZ} on output 20, check 99, \mathrm{CZ} on output 21, output 23, \mathrm{CZ} on output 21, output 24, \mathrm{CZ} on output 21, output 27, \mathrm{CZ} on output 21, output 35, \mathrm{CZ} on output 21, output 42, \mathrm{CZ} on output 21, output 43, \mathrm{CZ} on output 21, output 47, \mathrm{CZ} on output 21, output 51, \mathrm{CZ} on output 21, output 52, \mathrm{CZ} on output 21, output 53, \mathrm{CZ} on output 21, output 55, \mathrm{CZ} on output 21, output 56, \mathrm{CZ} on output 21, output 60, \mathrm{CZ} on output 21, output 61, \mathrm{CZ} on output 21, output 62, \mathrm{CZ} on output 21, output 64, \mathrm{CZ} on output 21, output 66, \mathrm{CZ} on output 21, output 69, \mathrm{CZ} on output 21, output 70, \mathrm{CZ} on output 21, output 73, \mathrm{CZ} on output 21, output 74, \mathrm{CZ} on output 21, output 75, \mathrm{CZ} on output 21, output 77, \mathrm{CZ} on output 21, output 78, \mathrm{CZ} on output 21, output 79, \mathrm{CZ} on output 21, check 80, \mathrm{CZ} on output 21, check 81, \mathrm{CZ} on output 21, check 82, \mathrm{CZ} on output 21, check 88, \mathrm{CZ} on output 21, check 92, \mathrm{CZ} on output 21, check 93, \mathrm{CZ} on output 21, check 94, \mathrm{CZ} on output 21, check 95, \mathrm{CZ} on output 21, check 99, \mathrm{CZ} on output 23, output 24, \mathrm{CZ} on output 23, output 25, \mathrm{CZ} on output 23, output 28, \mathrm{CZ} on output 23, output 34, \mathrm{CZ} on output 23, output 35, \mathrm{CZ} on output 23, output 37, \mathrm{CZ} on output 23, output 38, \mathrm{CZ} on output 23, output 41, \mathrm{CZ} on output 23, output 42, \mathrm{CZ} on output 23, output 48, \mathrm{CZ} on output 23, output 50, \mathrm{CZ} on output 23, output 51, \mathrm{CZ} on output 23, output 52, \mathrm{CZ} on output 23, output 57, \mathrm{CZ} on output 23, output 59, \mathrm{CZ} on output 23, output 61, \mathrm{CZ} on output 23, output 68, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, output 77, \mathrm{CZ} on output 23, output 78, \mathrm{CZ} on output 23, check 80, \mathrm{CZ} on output 23, check 81, \mathrm{CZ} on output 23, check 85, \mathrm{CZ} on output 23, check 90, \mathrm{CZ} on output 23, check 92, \mathrm{CZ} on output 23, check 97, \mathrm{CZ} on output 24, output 27, \mathrm{CZ} on output 24, output 35, \mathrm{CZ} on output 24, output 42, \mathrm{CZ} on output 24, output 43, \mathrm{CZ} on output 24, output 47, \mathrm{CZ} on output 24, output 51, \mathrm{CZ} on output 24, output 52, \mathrm{CZ} on output 24, output 53, \mathrm{CZ} on output 24, output 55, \mathrm{CZ} on output 24, output 56, \mathrm{CZ} on output 24, output 60, \mathrm{CZ} on output 24, output 61, \mathrm{CZ} on output 24, output 62, \mathrm{CZ} on output 24, output 64, \mathrm{CZ} on output 24, output 66, \mathrm{CZ} on output 24, output 69, \mathrm{CZ} on output 24, output 70, \mathrm{CZ} on output 24, output 73, \mathrm{CZ} on output 24, output 74, \mathrm{CZ} on output 24, output 75, \mathrm{CZ} on output 24, output 77, \mathrm{CZ} on output 24, output 78, \mathrm{CZ} on output 24, output 79, \mathrm{CZ} on output 24, check 80, \mathrm{CZ} on output 24, check 81, \mathrm{CZ} on output 24, check 82, \mathrm{CZ} on output 24, check 88, \mathrm{CZ} on output 24, check 92, \mathrm{CZ} on output 24, check 93, \mathrm{CZ} on output 24, check 94, \mathrm{CZ} on output 24, check 95, \mathrm{CZ} on output 24, check 99, \mathrm{CZ} on output 25, output 27, \mathrm{CZ} on output 25, output 28, \mathrm{CZ} on output 25, output 34, \mathrm{CZ} on output 25, output 37, \mathrm{CZ} on output 25, output 38, \mathrm{CZ} on output 25, output 41, \mathrm{CZ} on output 25, output 43, \mathrm{CZ} on output 25, output 47, \mathrm{CZ} on output 25, output 48, \mathrm{CZ} on output 25, output 50, \mathrm{CZ} on output 25, output 53, \mathrm{CZ} on output 25, output 55, \mathrm{CZ} on output 25, output 56, \mathrm{CZ} on output 25, output 57, \mathrm{CZ} on output 25, output 59, \mathrm{CZ} on output 25, output 60, \mathrm{CZ} on output 25, output 62, \mathrm{CZ} on output 25, output 64, \mathrm{CZ} on output 25, output 66, \mathrm{CZ} on output 25, output 68, \mathrm{CZ} on output 25, output 70, \mathrm{CZ} on output 25, output 73, \mathrm{CZ} on output 25, output 74, \mathrm{CZ} on output 25, output 75, \mathrm{CZ} on output 25, output 79, \mathrm{CZ} on output 25, check 82, \mathrm{CZ} on output 25, check 85, \mathrm{CZ} on output 25, check 88, \mathrm{CZ} on output 25, check 90, \mathrm{CZ} on output 25, check 93, \mathrm{CZ} on output 25, check 94, \mathrm{CZ} on output 25, check 95, \mathrm{CZ} on output 25, check 97, \mathrm{CZ} on output 25, check 99, \mathrm{CZ} on output 27, output 28, \mathrm{CZ} on output 27, output 34, \mathrm{CZ} on output 27, output 35, \mathrm{CZ} on output 27, output 37, \mathrm{CZ} on output 27, output 38, \mathrm{CZ} on output 27, output 41, \mathrm{CZ} on output 27, output 42, \mathrm{CZ} on output 27, output 48, \mathrm{CZ} on output 27, output 50, \mathrm{CZ} on output 27, output 51, \mathrm{CZ} on output 27, output 52, \mathrm{CZ} on output 27, output 57, \mathrm{CZ} on output 27, output 59, \mathrm{CZ} on output 27, output 61, \mathrm{CZ} on output 27, output 68, \mathrm{CZ} on output 27, output 69, \mathrm{CZ} on output 27, output 77, \mathrm{CZ} on output 27, output 78, \mathrm{CZ} on output 27, check 80, \mathrm{CZ} on output 27, check 81, \mathrm{CZ} on output 27, check 85, \mathrm{CZ} on output 27, check 90, \mathrm{CZ} on output 27, check 92, \mathrm{CZ} on output 27, check 97, \mathrm{CZ} on output 28, output 34, \mathrm{CZ} on output 28, output 37, \mathrm{CZ} on output 28, output 38, \mathrm{CZ} on output 28, output 41, \mathrm{CZ} on output 28, output 43, \mathrm{CZ} on output 28, output 47, \mathrm{CZ} on output 28, output 48, \mathrm{CZ} on output 28, output 50, \mathrm{CZ} on output 28, output 53, \mathrm{CZ} on output 28, output 55, \mathrm{CZ} on output 28, output 56, \mathrm{CZ} on output 28, output 57, \mathrm{CZ} on output 28, output 59, \mathrm{CZ} on output 28, output 60, \mathrm{CZ} on output 28, output 62, \mathrm{CZ} on output 28, output 64, \mathrm{CZ} on output 28, output 66, \mathrm{CZ} on output 28, output 68, \mathrm{CZ} on output 28, output 70, \mathrm{CZ} on output 28, output 73, \mathrm{CZ} on output 28, output 74, \mathrm{CZ} on output 28, output 75, \mathrm{CZ} on output 28, output 79, \mathrm{CZ} on output 28, check 82, \mathrm{CZ} on output 28, check 85, \mathrm{CZ} on output 28, check 88, \mathrm{CZ} on output 28, check 90, \mathrm{CZ} on output 28, check 93, \mathrm{CZ} on output 28, check 94, \mathrm{CZ} on output 28, check 95, \mathrm{CZ} on output 28, check 97, \mathrm{CZ} on output 28, check 99, \mathrm{CZ} on output 34, output 37, \mathrm{CZ} on output 34, output 38, \mathrm{CZ} on output 34, output 41, \mathrm{CZ} on output 34, output 43, \mathrm{CZ} on output 34, output 47, \mathrm{CZ} on output 34, output 48, \mathrm{CZ} on output 34, output 50, \mathrm{CZ} on output 34, output 53, \mathrm{CZ} on output 34, output 55, \mathrm{CZ} on output 34, output 56, \mathrm{CZ} on output 34, output 57, \mathrm{CZ} on output 34, output 59, \mathrm{CZ} on output 34, output 60, \mathrm{CZ} on output 34, output 62, \mathrm{CZ} on output 34, output 64, \mathrm{CZ} on output 34, output 66, \mathrm{CZ} on output 34, output 68, \mathrm{CZ} on output 34, output 70, \mathrm{CZ} on output 34, output 73, \mathrm{CZ} on output 34, output 74, \mathrm{CZ} on output 34, output 75, \mathrm{CZ} on output 34, output 79, \mathrm{CZ} on output 34, check 82, \mathrm{CZ} on output 34, check 85, \mathrm{CZ} on output 34, check 88, \mathrm{CZ} on output 34, check 90, \mathrm{CZ} on output 34, check 93, \mathrm{CZ} on output 34, check 94, \mathrm{CZ} on output 34, check 95, \mathrm{CZ} on output 34, check 97, \mathrm{CZ} on output 34, check 99, \mathrm{CZ} on output 35, output 42, \mathrm{CZ} on output 35, output 43, \mathrm{CZ} on output 35, output 47, \mathrm{CZ} on output 35, output 51, \mathrm{CZ} on output 35, output 52, \mathrm{CZ} on output 35, output 53, \mathrm{CZ} on output 35, output 55, \mathrm{CZ} on output 35, output 56, \mathrm{CZ} on output 35, output 60, \mathrm{CZ} on output 35, output 61, \mathrm{CZ} on output 35, output 62, \mathrm{CZ} on output 35, output 64, \mathrm{CZ} on output 35, output 66, \mathrm{CZ} on output 35, output 69, \mathrm{CZ} on output 35, output 70, \mathrm{CZ} on output 35, output 73, \mathrm{CZ} on output 35, output 74, \mathrm{CZ} on output 35, output 75, \mathrm{CZ} on output 35, output 77, \mathrm{CZ} on output 35, output 78, \mathrm{CZ} on output 35, output 79, \mathrm{CZ} on output 35, check 80, \mathrm{CZ} on output 35, check 81, \mathrm{CZ} on output 35, check 82, \mathrm{CZ} on output 35, check 88, \mathrm{CZ} on output 35, check 92, \mathrm{CZ} on output 35, check 93, \mathrm{CZ} on output 35, check 94, \mathrm{CZ} on output 35, check 95, \mathrm{CZ} on output 35, check 99, \mathrm{CZ} on output 37, output 38, \mathrm{CZ} on output 37, output 41, \mathrm{CZ} on output 37, output 43, \mathrm{CZ} on output 37, output 47, \mathrm{CZ} on output 37, output 48, \mathrm{CZ} on output 37, output 50, \mathrm{CZ} on output 37, output 53, \mathrm{CZ} on output 37, output 55, \mathrm{CZ} on output 37, output 56, \mathrm{CZ} on output 37, output 57, \mathrm{CZ} on output 37, output 59, \mathrm{CZ} on output 37, output 60, \mathrm{CZ} on output 37, output 62, \mathrm{CZ} on output 37, output 64, \mathrm{CZ} on output 37, output 66, \mathrm{CZ} on output 37, output 68, \mathrm{CZ} on output 37, output 70, \mathrm{CZ} on output 37, output 73, \mathrm{CZ} on output 37, output 74, \mathrm{CZ} on output 37, output 75, \mathrm{CZ} on output 37, output 79, \mathrm{CZ} on output 37, check 82, \mathrm{CZ} on output 37, check 85, \mathrm{CZ} on output 37, check 88, \mathrm{CZ} on output 37, check 90, \mathrm{CZ} on output 37, check 93, \mathrm{CZ} on output 37, check 94, \mathrm{CZ} on output 37, check 95, \mathrm{CZ} on output 37, check 97, \mathrm{CZ} on output 37, check 99, \mathrm{CZ} on output 38, output 41, \mathrm{CZ} on output 38, output 43, \mathrm{CZ} on output 38, output 47, \mathrm{CZ} on output 38, output 48, \mathrm{CZ} on output 38, output 50, \mathrm{CZ} on output 38, output 53, \mathrm{CZ} on output 38, output 55, \mathrm{CZ} on output 38, output 56, \mathrm{CZ} on output 38, output 57, \mathrm{CZ} on output 38, output 59, \mathrm{CZ} on output 38, output 60, \mathrm{CZ} on output 38, output 62, \mathrm{CZ} on output 38, output 64, \mathrm{CZ} on output 38, output 66, \mathrm{CZ} on output 38, output 68, \mathrm{CZ} on output 38, output 70, \mathrm{CZ} on output 38, output 73, \mathrm{CZ} on output 38, output 74, \mathrm{CZ} on output 38, output 75, \mathrm{CZ} on output 38, output 79, \mathrm{CZ} on output 38, check 82, \mathrm{CZ} on output 38, check 85, \mathrm{CZ} on output 38, check 88, \mathrm{CZ} on output 38, check 90, \mathrm{CZ} on output 38, check 93, \mathrm{CZ} on output 38, check 94, \mathrm{CZ} on output 38, check 95, \mathrm{CZ} on output 38, check 97, \mathrm{CZ} on output 38, check 99, \mathrm{CZ} on output 41, output 43, \mathrm{CZ} on output 41, output 47, \mathrm{CZ} on output 41, output 48, \mathrm{CZ} on output 41, output 50, \mathrm{CZ} on output 41, output 53, \mathrm{CZ} on output 41, output 55, \mathrm{CZ} on output 41, output 56, \mathrm{CZ} on output 41, output 57, \mathrm{CZ} on output 41, output 59, \mathrm{CZ} on output 41, output 60, \mathrm{CZ} on output 41, output 62, \mathrm{CZ} on output 41, output 64, \mathrm{CZ} on output 41, output 66, \mathrm{CZ} on output 41, output 68, \mathrm{CZ} on output 41, output 70, \mathrm{CZ} on output 41, output 73, \mathrm{CZ} on output 41, output 74, \mathrm{CZ} on output 41, output 75, \mathrm{CZ} on output 41, output 79, \mathrm{CZ} on output 41, check 82, \mathrm{CZ} on output 41, check 85, \mathrm{CZ} on output 41, check 88, \mathrm{CZ} on output 41, check 90, \mathrm{CZ} on output 41, check 93, \mathrm{CZ} on output 41, check 94, \mathrm{CZ} on output 41, check 95, \mathrm{CZ} on output 41, check 97, \mathrm{CZ} on output 41, check 99, \mathrm{CZ} on output 42, output 43, \mathrm{CZ} on output 42, output 47, \mathrm{CZ} on output 42, output 51, \mathrm{CZ} on output 42, output 52, \mathrm{CZ} on output 42, output 53, \mathrm{CZ} on output 42, output 55, \mathrm{CZ} on output 42, output 56, \mathrm{CZ} on output 42, output 60, \mathrm{CZ} on output 42, output 61, \mathrm{CZ} on output 42, output 62, \mathrm{CZ} on output 42, output 64, \mathrm{CZ} on output 42, output 66, \mathrm{CZ} on output 42, output 69, \mathrm{CZ} on output 42, output 70, \mathrm{CZ} on output 42, output 73, \mathrm{CZ} on output 42, output 74, \mathrm{CZ} on output 42, output 75, \mathrm{CZ} on output 42, output 77, \mathrm{CZ} on output 42, output 78, \mathrm{CZ} on output 42, output 79, \mathrm{CZ} on output 42, check 80, \mathrm{CZ} on output 42, check 81, \mathrm{CZ} on output 42, check 82, \mathrm{CZ} on output 42, check 88, \mathrm{CZ} on output 42, check 92, \mathrm{CZ} on output 42, check 93, \mathrm{CZ} on output 42, check 94, \mathrm{CZ} on output 42, check 95, \mathrm{CZ} on output 42, check 99, \mathrm{CZ} on output 43, output 48, \mathrm{CZ} on output 43, output 50, \mathrm{CZ} on output 43, output 51, \mathrm{CZ} on output 43, output 52, \mathrm{CZ} on output 43, output 57, \mathrm{CZ} on output 43, output 59, \mathrm{CZ} on output 43, output 61, \mathrm{CZ} on output 43, output 68, \mathrm{CZ} on output 43, output 69, \mathrm{CZ} on output 43, output 77, \mathrm{CZ} on output 43, output 78, \mathrm{CZ} on output 43, check 80, \mathrm{CZ} on output 43, check 81, \mathrm{CZ} on output 43, check 85, \mathrm{CZ} on output 43, check 90, \mathrm{CZ} on output 43, check 92, \mathrm{CZ} on output 43, check 97, \mathrm{CZ} on output 47, output 48, \mathrm{CZ} on output 47, output 50, \mathrm{CZ} on output 47, output 51, \mathrm{CZ} on output 47, output 52, \mathrm{CZ} on output 47, output 57, \mathrm{CZ} on output 47, output 59, \mathrm{CZ} on output 47, output 61, \mathrm{CZ} on output 47, output 68, \mathrm{CZ} on output 47, output 69, \mathrm{CZ} on output 47, output 77, \mathrm{CZ} on output 47, output 78, \mathrm{CZ} on output 47, check 80, \mathrm{CZ} on output 47, check 81, \mathrm{CZ} on output 47, check 85, \mathrm{CZ} on output 47, check 90, \mathrm{CZ} on output 47, check 92, \mathrm{CZ} on output 47, check 97, \mathrm{CZ} on output 48, output 50, \mathrm{CZ} on output 48, output 53, \mathrm{CZ} on output 48, output 55, \mathrm{CZ} on output 48, output 56, \mathrm{CZ} on output 48, output 57, \mathrm{CZ} on output 48, output 59, \mathrm{CZ} on output 48, output 60, \mathrm{CZ} on output 48, output 62, \mathrm{CZ} on output 48, output 64, \mathrm{CZ} on output 48, output 66, \mathrm{CZ} on output 48, output 68, \mathrm{CZ} on output 48, output 70, \mathrm{CZ} on output 48, output 73, \mathrm{CZ} on output 48, output 74, \mathrm{CZ} on output 48, output 75, \mathrm{CZ} on output 48, output 79, \mathrm{CZ} on output 48, check 82, \mathrm{CZ} on output 48, check 85, \mathrm{CZ} on output 48, check 88, \mathrm{CZ} on output 48, check 90, \mathrm{CZ} on output 48, check 93, \mathrm{CZ} on output 48, check 94, \mathrm{CZ} on output 48, check 95, \mathrm{CZ} on output 48, check 97, \mathrm{CZ} on output 48, check 99, \mathrm{CZ} on output 50, output 53, \mathrm{CZ} on output 50, output 55, \mathrm{CZ} on output 50, output 56, \mathrm{CZ} on output 50, output 57, \mathrm{CZ} on output 50, output 59, \mathrm{CZ} on output 50, output 60, \mathrm{CZ} on output 50, output 62, \mathrm{CZ} on output 50, output 64, \mathrm{CZ} on output 50, output 66, \mathrm{CZ} on output 50, output 68, \mathrm{CZ} on output 50, output 70, \mathrm{CZ} on output 50, output 73, \mathrm{CZ} on output 50, output 74, \mathrm{CZ} on output 50, output 75, \mathrm{CZ} on output 50, output 79, \mathrm{CZ} on output 50, check 82, \mathrm{CZ} on output 50, check 85, \mathrm{CZ} on output 50, check 88, \mathrm{CZ} on output 50, check 90, \mathrm{CZ} on output 50, check 93, \mathrm{CZ} on output 50, check 94, \mathrm{CZ} on output 50, check 95, \mathrm{CZ} on output 50, check 97, \mathrm{CZ} on output 50, check 99, \mathrm{CZ} on output 51, output 52, \mathrm{CZ} on output 51, output 53, \mathrm{CZ} on output 51, output 55, \mathrm{CZ} on output 51, output 56, \mathrm{CZ} on output 51, output 60, \mathrm{CZ} on output 51, output 61, \mathrm{CZ} on output 51, output 62, \mathrm{CZ} on output 51, output 64, \mathrm{CZ} on output 51, output 66, \mathrm{CZ} on output 51, output 69, \mathrm{CZ} on output 51, output 70, \mathrm{CZ} on output 51, output 73, \mathrm{CZ} on output 51, output 74, \mathrm{CZ} on output 51, output 75, \mathrm{CZ} on output 51, output 77, \mathrm{CZ} on output 51, output 78, \mathrm{CZ} on output 51, output 79, \mathrm{CZ} on output 51, check 80, \mathrm{CZ} on output 51, check 81, \mathrm{CZ} on output 51, check 82, \mathrm{CZ} on output 51, check 88, \mathrm{CZ} on output 51, check 92, \mathrm{CZ} on output 51, check 93, \mathrm{CZ} on output 51, check 94, \mathrm{CZ} on output 51, check 95, \mathrm{CZ} on output 51, check 99, \mathrm{CZ} on output 52, output 53, \mathrm{CZ} on output 52, output 55, \mathrm{CZ} on output 52, output 56, \mathrm{CZ} on output 52, output 60, \mathrm{CZ} on output 52, output 61, \mathrm{CZ} on output 52, output 62, \mathrm{CZ} on output 52, output 64, \mathrm{CZ} on output 52, output 66, \mathrm{CZ} on output 52, output 69, \mathrm{CZ} on output 52, output 70, \mathrm{CZ} on output 52, output 73, \mathrm{CZ} on output 52, output 74, \mathrm{CZ} on output 52, output 75, \mathrm{CZ} on output 52, output 77, \mathrm{CZ} on output 52, output 78, \mathrm{CZ} on output 52, output 79, \mathrm{CZ} on output 52, check 80, \mathrm{CZ} on output 52, check 81, \mathrm{CZ} on output 52, check 82, \mathrm{CZ} on output 52, check 88, \mathrm{CZ} on output 52, check 92, \mathrm{CZ} on output 52, check 93, \mathrm{CZ} on output 52, check 94, \mathrm{CZ} on output 52, check 95, \mathrm{CZ} on output 52, check 99, \mathrm{CZ} on output 53, output 57, \mathrm{CZ} on output 53, output 59, \mathrm{CZ} on output 53, output 61, \mathrm{CZ} on output 53, output 68, \mathrm{CZ} on output 53, output 69, \mathrm{CZ} on output 53, output 77, \mathrm{CZ} on output 53, output 78, \mathrm{CZ} on output 53, check 80, \mathrm{CZ} on output 53, check 81, \mathrm{CZ} on output 53, check 85, \mathrm{CZ} on output 53, check 90, \mathrm{CZ} on output 53, check 92, \mathrm{CZ} on output 53, check 97, \mathrm{CZ} on output 55, output 57, \mathrm{CZ} on output 55, output 59, \mathrm{CZ} on output 55, output 61, \mathrm{CZ} on output 55, output 68, \mathrm{CZ} on output 55, output 69, \mathrm{CZ} on output 55, output 77, \mathrm{CZ} on output 55, output 78, \mathrm{CZ} on output 55, check 80, \mathrm{CZ} on output 55, check 81, \mathrm{CZ} on output 55, check 85, \mathrm{CZ} on output 55, check 90, \mathrm{CZ} on output 55, check 92, \mathrm{CZ} on output 55, check 97, \mathrm{CZ} on output 56, output 57, \mathrm{CZ} on output 56, output 59, \mathrm{CZ} on output 56, output 61, \mathrm{CZ} on output 56, output 68, \mathrm{CZ} on output 56, output 69, \mathrm{CZ} on output 56, output 77, \mathrm{CZ} on output 56, output 78, \mathrm{CZ} on output 56, check 80, \mathrm{CZ} on output 56, check 81, \mathrm{CZ} on output 56, check 85, \mathrm{CZ} on output 56, check 90, \mathrm{CZ} on output 56, check 92, \mathrm{CZ} on output 56, check 97, \mathrm{CZ} on output 57, output 59, \mathrm{CZ} on output 57, output 60, \mathrm{CZ} on output 57, output 62, \mathrm{CZ} on output 57, output 64, \mathrm{CZ} on output 57, output 66, \mathrm{CZ} on output 57, output 68, \mathrm{CZ} on output 57, output 70, \mathrm{CZ} on output 57, output 73, \mathrm{CZ} on output 57, output 74, \mathrm{CZ} on output 57, output 75, \mathrm{CZ} on output 57, output 79, \mathrm{CZ} on output 57, check 82, \mathrm{CZ} on output 57, check 85, \mathrm{CZ} on output 57, check 88, \mathrm{CZ} on output 57, check 90, \mathrm{CZ} on output 57, check 93, \mathrm{CZ} on output 57, check 94, \mathrm{CZ} on output 57, check 95, \mathrm{CZ} on output 57, check 97, \mathrm{CZ} on output 57, check 99, \mathrm{CZ} on output 59, output 60, \mathrm{CZ} on output 59, output 62, \mathrm{CZ} on output 59, output 64, \mathrm{CZ} on output 59, output 66, \mathrm{CZ} on output 59, output 68, \mathrm{CZ} on output 59, output 70, \mathrm{CZ} on output 59, output 73, \mathrm{CZ} on output 59, output 74, \mathrm{CZ} on output 59, output 75, \mathrm{CZ} on output 59, output 79, \mathrm{CZ} on output 59, check 82, \mathrm{CZ} on output 59, check 85, \mathrm{CZ} on output 59, check 88, \mathrm{CZ} on output 59, check 90, \mathrm{CZ} on output 59, check 93, \mathrm{CZ} on output 59, check 94, \mathrm{CZ} on output 59, check 95, \mathrm{CZ} on output 59, check 97, \mathrm{CZ} on output 59, check 99, \mathrm{CZ} on output 60, output 61, \mathrm{CZ} on output 60, output 68, \mathrm{CZ} on output 60, output 69, \mathrm{CZ} on output 60, output 77, \mathrm{CZ} on output 60, output 78, \mathrm{CZ} on output 60, check 80, \mathrm{CZ} on output 60, check 81, \mathrm{CZ} on output 60, check 85, \mathrm{CZ} on output 60, check 90, \mathrm{CZ} on output 60, check 92, \mathrm{CZ} on output 60, check 97, \mathrm{CZ} on output 61, output 62, \mathrm{CZ} on output 61, output 64, \mathrm{CZ} on output 61, output 66, \mathrm{CZ} on output 61, output 69, \mathrm{CZ} on output 61, output 70, \mathrm{CZ} on output 61, output 73, \mathrm{CZ} on output 61, output 74, \mathrm{CZ} on output 61, output 75, \mathrm{CZ} on output 61, output 77, \mathrm{CZ} on output 61, output 78, \mathrm{CZ} on output 61, output 79, \mathrm{CZ} on output 61, check 80, \mathrm{CZ} on output 61, check 81, \mathrm{CZ} on output 61, check 82, \mathrm{CZ} on output 61, check 88, \mathrm{CZ} on output 61, check 92, \mathrm{CZ} on output 61, check 93, \mathrm{CZ} on output 61, check 94, \mathrm{CZ} on output 61, check 95, \mathrm{CZ} on output 61, check 99, \mathrm{CZ} on output 62, output 68, \mathrm{CZ} on output 62, output 69, \mathrm{CZ} on output 62, output 77, \mathrm{CZ} on output 62, output 78, \mathrm{CZ} on output 62, check 80, \mathrm{CZ} on output 62, check 81, \mathrm{CZ} on output 62, check 85, \mathrm{CZ} on output 62, check 90, \mathrm{CZ} on output 62, check 92, \mathrm{CZ} on output 62, check 97, \mathrm{CZ} on output 64, output 68, \mathrm{CZ} on output 64, output 69, \mathrm{CZ} on output 64, output 77, \mathrm{CZ} on output 64, output 78, \mathrm{CZ} on output 64, check 80, \mathrm{CZ} on output 64, check 81, \mathrm{CZ} on output 64, check 85, \mathrm{CZ} on output 64, check 90, \mathrm{CZ} on output 64, check 92, \mathrm{CZ} on output 64, check 97, \mathrm{CZ} on output 66, output 68, \mathrm{CZ} on output 66, output 69, \mathrm{CZ} on output 66, output 77, \mathrm{CZ} on output 66, output 78, \mathrm{CZ} on output 66, check 80, \mathrm{CZ} on output 66, check 81, \mathrm{CZ} on output 66, check 85, \mathrm{CZ} on output 66, check 90, \mathrm{CZ} on output 66, check 92, \mathrm{CZ} on output 66, check 97, \mathrm{CZ} on output 68, output 70, \mathrm{CZ} on output 68, output 73, \mathrm{CZ} on output 68, output 74, \mathrm{CZ} on output 68, output 75, \mathrm{CZ} on output 68, output 79, \mathrm{CZ} on output 68, check 82, \mathrm{CZ} on output 68, check 85, \mathrm{CZ} on output 68, check 88, \mathrm{CZ} on output 68, check 90, \mathrm{CZ} on output 68, check 93, \mathrm{CZ} on output 68, check 94, \mathrm{CZ} on output 68, check 95, \mathrm{CZ} on output 68, check 97, \mathrm{CZ} on output 68, check 99, \mathrm{CZ} on output 69, output 70, \mathrm{CZ} on output 69, output 73, \mathrm{CZ} on output 69, output 74, \mathrm{CZ} on output 69, output 75, \mathrm{CZ} on output 69, output 77, \mathrm{CZ} on output 69, output 78, \mathrm{CZ} on output 69, output 79, \mathrm{CZ} on output 69, check 80, \mathrm{CZ} on output 69, check 81, \mathrm{CZ} on output 69, check 82, \mathrm{CZ} on output 69, check 88, \mathrm{CZ} on output 69, check 92, \mathrm{CZ} on output 69, check 93, \mathrm{CZ} on output 69, check 94, \mathrm{CZ} on output 69, check 95, \mathrm{CZ} on output 69, check 99, \mathrm{CZ} on output 70, output 77, \mathrm{CZ} on output 70, output 78, \mathrm{CZ} on output 70, check 80, \mathrm{CZ} on output 70, check 81, \mathrm{CZ} on output 70, check 85, \mathrm{CZ} on output 70, check 90, \mathrm{CZ} on output 70, check 92, \mathrm{CZ} on output 70, check 97, \mathrm{CZ} on output 73, output 77, \mathrm{CZ} on output 73, output 78, \mathrm{CZ} on output 73, check 80, \mathrm{CZ} on output 73, check 81, \mathrm{CZ} on output 73, check 85, \mathrm{CZ} on output 73, check 90, \mathrm{CZ} on output 73, check 92, \mathrm{CZ} on output 73, check 97, \mathrm{CZ} on output 74, output 77, \mathrm{CZ} on output 74, output 78, \mathrm{CZ} on output 74, check 80, \mathrm{CZ} on output 74, check 81, \mathrm{CZ} on output 74, check 85, \mathrm{CZ} on output 74, check 90, \mathrm{CZ} on output 74, check 92, \mathrm{CZ} on output 74, check 97, \mathrm{CZ} on output 75, output 77, \mathrm{CZ} on output 75, output 78, \mathrm{CZ} on output 75, check 80, \mathrm{CZ} on output 75, check 81, \mathrm{CZ} on output 75, check 85, \mathrm{CZ} on output 75, check 90, \mathrm{CZ} on output 75, check 92, \mathrm{CZ} on output 75, check 97, \mathrm{CZ} on output 77, output 78, \mathrm{CZ} on output 77, output 79, \mathrm{CZ} on output 77, check 80, \mathrm{CZ} on output 77, check 81, \mathrm{CZ} on output 77, check 82, \mathrm{CZ} on output 77, check 88, \mathrm{CZ} on output 77, check 92, \mathrm{CZ} on output 77, check 93, \mathrm{CZ} on output 77, check 94, \mathrm{CZ} on output 77, check 95, \mathrm{CZ} on output 77, check 99, \mathrm{CZ} on output 78, output 79, \mathrm{CZ} on output 78, check 80, \mathrm{CZ} on output 78, check 81, \mathrm{CZ} on output 78, check 82, \mathrm{CZ} on output 78, check 88, \mathrm{CZ} on output 78, check 92, \mathrm{CZ} on output 78, check 93, \mathrm{CZ} on output 78, check 94, \mathrm{CZ} on output 78, check 95, \mathrm{CZ} on output 78, check 99, \mathrm{CZ} on output 79, check 80, \mathrm{CZ} on output 79, check 81, \mathrm{CZ} on output 79, check 85, \mathrm{CZ} on output 79, check 90, \mathrm{CZ} on output 79, check 92, \mathrm{CZ} on output 79, check 97, \mathrm{CZ} on check 80, check 81, \mathrm{CZ} on check 80, check 82, \mathrm{CZ} on check 80, check 88, \mathrm{CZ} on check 80, check 92, \mathrm{CZ} on check 80, check 93, \mathrm{CZ} on check 80, check 94, \mathrm{CZ} on check 80, check 95, \mathrm{CZ} on check 80, check 99, \mathrm{CZ} on check 81, check 82, \mathrm{CZ} on check 81, check 88, \mathrm{CZ} on check 81, check 92, \mathrm{CZ} on check 81, check 93, \mathrm{CZ} on check 81, check 94, \mathrm{CZ} on check 81, check 95, \mathrm{CZ} on check 81, check 99, \mathrm{CZ} on check 82, check 85, \mathrm{CZ} on check 82, check 90, \mathrm{CZ} on check 82, check 92, \mathrm{CZ} on check 82, check 97, \mathrm{CZ} on check 85, check 88, \mathrm{CZ} on check 85, check 90, \mathrm{CZ} on check 85, check 93, \mathrm{CZ} on check 85, check 94, \mathrm{CZ} on check 85, check 95, \mathrm{CZ} on check 85, check 97, \mathrm{CZ} on check 85, check 99, \mathrm{CZ} on check 88, check 90, \mathrm{CZ} on check 88, check 92, \mathrm{CZ} on check 88, check 97, \mathrm{CZ} on check 90, check 93, \mathrm{CZ} on check 90, check 94, \mathrm{CZ} on check 90, check 95, \mathrm{CZ} on check 90, check 97, \mathrm{CZ} on check 90, check 99, \mathrm{CZ} on check 92, check 93, \mathrm{CZ} on check 92, check 94, \mathrm{CZ} on check 92, check 95, \mathrm{CZ} on check 92, check 99, \mathrm{CZ} on check 93, check 97, \mathrm{CZ} on check 94, check 97, \mathrm{CZ} on check 95, check 97, \mathrm{CZ} on check 97, check 99

Or no Clifford gate at all: run \mathrm{T}^3 on rotations 4, 6, 15, 16, 17, 27, 38, 41, 44, 53, 55, 56, 57, 60, 62, 64, 65, 76, 78, 83, 88, 89, 98, 99 and 126 more (listed below); \mathrm{T}^5 on rotations 0, 1, 2, 7, 10, 11, 12, 20, 22, 25, 32, 34, 36, 46, 52, 84, 90, 101, 105, 106, 109, 112, 127, 140 and 4 more (listed below); \mathrm{T}^\dagger on rotations 3, 5, 9, 13, 18, 19, 21, 30, 31, 33, 35, 40, 42, 66, 71, 80, 113, 114, 115, 119, 128, 130, 134, 155, and \mathrm{T} on the rest. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.

All 150 rotations at T³

4, 6, 15, 16, 17, 27, 38, 41, 44, 53, 55, 56, 57, 60, 62, 64, 65, 76, 78, 83, 88, 89, 98, 99, 100, 102, 103, 107, 108, 111, 121, 125, 131, 132, 136, 143, 148, 149, 150, 151, 152, 157, 159, 161, 163, 165, 169, 170, 177, 179, 180, 181, 182, 185, 188, 191, 192, 193, 195, 197, 198, 202, 205, 206, 212, 215, 217, 219, 226, 228, 229, 230, 231, 233, 239, 242, 243, 246, 251, 254, 256, 257, 258, 260, 261, 262, 264, 266, 269, 270, 277, 282, 283, 284, 286, 289, 293, 296, 297, 302, 304, 306, 308, 314, 318, 319, 320, 325, 327, 330, 335, 336, 340, 341, 342, 344, 345, 347, 351, 353, 356, 358, 359, 361, 363, 364, 365, 372, 373, 376, 378, 380, 383, 385, 388, 389, 390, 391, 392, 394, 401, 402, 404, 408, 409, 415, 417, 421, 424, 427

All 28 rotations at T⁵

0, 1, 2, 7, 10, 11, 12, 20, 22, 25, 32, 34, 36, 46, 52, 84, 90, 101, 105, 106, 109, 112, 127, 140, 154, 158, 168, 213

Rotations are numbered by matrix column, from 0. The correction comes from the columns by the weight expansion of Bravyi and Haah (2012). verify_catalog.py re-derives it, checks the corrected circuit's phase input by input against the gate, and on small circuits simulates it gate by gate.

Convert the output with CNOT and S

A CNOT circuit on the outputs, followed by S, Z and CZ gates, turns this factory's gate into other gates that prepare the same magic state. Type a target gate to check whether it is reachable. If it is, you get the circuit, checked on every basis state.

Or list every gate it reaches. The list is built in your browser and saved as a text file, one gate per line.

Python code that writes the same list
import json, urllib.request

NAMES = {1: "T", 2: "CS", 3: "CCZ"}


def equivalent_gates(k, terms, limit=1_000_000):
    """Every gate a CNOT circuit and S, Z, CZ gates reach from this one.

    A gate is its set of terms mod Clifford: {a} is T, {a,b} is CS and
    {a,b,c} is CCZ on those outputs. CNOT c->t sends x_t to
    x_c + x_t - 2 x_c x_t, so a term on t but not c adds the term with t
    replaced by c, and, below CCZ, the term with c added.
    """
    start = frozenset(frozenset(m) for m in terms)
    seen, queue = {start}, [start]
    for gate in queue:
        for c in range(k):
            for t in range(k):
                if c == t:
                    continue
                new = set(gate)
                for m in gate:
                    if t in m and c not in m:
                        new ^= {(m - {t}) | {c}}
                        if len(m) < 3:
                            new ^= {m | {c}}
                new = frozenset(new)
                if new not in seen:
                    seen.add(new)
                    queue.append(new)
                    if len(seen) > limit:
                        raise RuntimeError(f"more than {limit} equivalent gates")
    return seen


def name(gate, k):
    sep = "," if k > 10 else ""
    terms = sorted((sorted(m) for m in gate), key=lambda m: (len(m), m))
    return "·".join(NAMES[len(m)] + sep.join(map(str, m)) for m in terms) or "I"


url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/428.80.4.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-428.80.4.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

d=4, exact. No fault of weight below 4 is both undetectable and damaging. One of weight 4 is.

Exactly 7,936 faults of weight 4 are undetectable and damaging, so A_{4}=7{,}936. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{4}\,p^{4}+O(p^{5}).

A damaging fault of weight 4 sits on columns [0,1,10,11].

A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.

Original source

S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535

Provenance

a paired-column contraction of an existing triorthogonal code, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows

Found by: AI search (gamma frontier): contraction of an existing code

Discovery: AI search

1 recorded source
[
 {
  "regime": "AI search (gamma frontier): contraction of an existing code",
  "file": "gamma_frontier_release/protocols/paired_column_contraction_428_80_4_0c04f8eae387.json",
  "label": "paired_column_contraction_428_80_4_0c04f8eae387",
  "N": 100,
  "d": 4,
  "d_is_exact": true,
  "origin": "Existing triorthogonal code with physical paired-column contraction",
  "provenance": "gamma frontier release record paired_column_contraction_428_80_4_0c04f8eae387 (source catalogue id paired_column_contraction_428_80_4_0c04f8eae387); construction: Existing triorthogonal code with physical paired-column contraction; matrix 0c04f8eae3877c2d...; the release states d=4 (exact), gamma=1.2097694457568924 (exact)",
  "notes": "matrix gamma_frontier_release/matrices/0c04f8eae3877c2deb7a092b3925299febebe26abbd99949791717a0eeb9f6cb.matrix"
 }
]

Use it in code

Load this factory and re-derive every number from its circuit with the catalogue's own verifier.

# git clone https://github.com/shubhamj810/magic-state-factory-repo
# cd magic-state-factory-repo/master_catalog
import json, urllib.request
import verify_catalog as VC

url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/428.80.4.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]

facts, problems = VC.derive(columns, k, N)    # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N)  # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
      problems or "verified")

Raw record

Show the JSON this page is built from

Source: master_catalog.json, factories[1047].