The circuit
The 101\times430 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.
| 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 (159) | ···11···1····1···11·······11·1·111···1111·11········1··1······11··1···11···11··11··1·1·1·····11···1·1···11····11·1·11·11··1·1111···11··111·1·1··1··11·11··1···1····1··1··11·········11·11·11···1··1·······11·1··111·····1··1····11······111····111··11·11·1·1············1··1········11··1···11·····1·11111····1·1····1···1····11·······11··1··1111··1·1111···11··11·1·11···1·11·11···1···1····1·1··11········11··11·11····1···1·······11·1··1 |
| 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····1·1·111111···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 (175) | ·····11··1··1·11111·1····1·1·1··1··11·1·111···1111··1·····1······11·1·1··11·1··1·······1·1···1·11·1······11··1·1·1··1··1·1··111·····1··111·1·111··1·111··11····1········111111··1·111111··1·····1·11···1··11·1··1··11····11·11·111·1···1·11·····1·11·1··111······111·1···1····1·········11··11·1··1·1·1···1··1·1···1·11·········11····1··1··1···1·1·1··111·····1··11·1·11·11·1·111···11····1·······111111···1111·11··1······1··1·1···1·11·1··1 |
| out 3 (173) | ·····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··111111······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··11·1·111·1·······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 (183) | ····11·111··1···111··1····11·11·1·····1111····1··11·11····1···1··1··1·1··1··1·1····1····1····111··1·1··111···1··11····11·1·1111·11··11··11·1·1111·11··111111·1·11··1····1··11·····11··11·11····1·1111··1·····1····11·1··111····111··1···111·1···1····1·111·······1···11··11···1······1··1···11·1····11··1··1···1·1·1··11··1···111·····1····11····11·1·1111·11··11··1·1·11·11111··111·1111··11··1···1··11····11···11·11·····1·1·1·11··1····1··· |
| out 6 (165) | ·····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·····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··1··11·1··1·1·1···11·1······1····11··1·1·1·1·····1·· |
| out 7 (173) | ···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·······1111·····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····1111·1···1··1··11······1111······1······1·1·1·111·1··11·1 |
| out 8 (175) | ···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···1·111··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····1·11·1111·111··1·1··11·11··1·111···1··1···1111···11····11·11·· |
| out 9 (173) | ·····1···1··11·1111·1·1··1·1·1·1·1·1·1··1··1··11··1·····11·11···11·11·11······1·1··1·1·11···1·111·11·1·11····111···11·11····11·1··11·······1··1·1·1·1·11··1··1··1·1···1·1··111·1·1··1·1111·······1···1····11·1·····1·····111·1·111·1·1·1·11····1·11·1···1···1····11···1······1·1·1·····11··1111······1·11111·····1·1·11·1··1··11······1·11·····1111····11·1··11········1··1·11·1·11···1·1···1·1··111··111·11··1··1111········1·····1···11·1··· |
| out 10 (173) | ···1··111···11·1·11··1···11····1····11111·111··11·1·1···11··1·11111······1··1·1·1····11·1···111····1·1·1111···1····11·11·11···11·111···1·1·1·1·······1··11······1·11··1·1·1····1··11·1··111·····111··1·····1··1·11··11··1·11·1··11··1··11······1···111·11·1·1·1···11··1··1···1···1···11111·····1····11·1·1·1···1·1······1··1··1111······1······1111·11···11·111···1··1·11·······1··1·1······1·11·1·1·1····1·11·1···111······11·1···1····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 (157) | ···11·1·····1·1···1·1·····1··11111··1·1·1···1·11111·1··1·1··1····1111·1··1·····11·1··1·11···1······1···11·1····11···1·1····1··1·1··111··11·1····1··111·11·1··11···1······11·11·1··1·······11·11·11···1········1··11·1·····1·1····1·1····1·1·1··111·1·1··1·····1··111·11··1··1····1······11·111·1······11·111············1·····11·1·······1·1····11····1··1·1··111··1·1·1····1·111·11··1·1·1···1·····11·11·1·1········111··1·11·····1·······1·· |
| out 13 (151) | ·····111····1·111·1·1·1···11····1·····1··111···1·11·1···1··11···1·1·1·····1···1·1··1···1······1·1·11·1·1111····1···1··1··1··111··11·11···1····111·····11·1···1····1······11·1····1·1··11·11·····1··11··1········1··111····1·11·1·1·1·1··11······1····1···11·1·····1··11··1···1·1·1·····1·1··1·····1··1·11·1······1···11·1··1··1111·······1····11·1··1··111··11·11····1····111····11··1··1·····1·····11·1···1·1···11·11······1····11··1·······1 |
| out 14 (181) | ············1111·11······11···1111···11····11·1111··1···111·1··11111···1111·1·1·1··1·1·111··11·······1·111····1111·1··11·1····111·111··1·1···1··1····1···1···1·1··1···1·111·11·1·1111···11·······11·11····11·1··1·········1111··11·····11···1··111··11······1·1··111·1···1···11··1····1111·1··11··1·11·11111·1·1···········1··111·······11·11··1·11·1····111·111··1··1··1···1···1····1··1··1··1··1·111·11·11111····11········1·1··11···11·1··1 |
| out 15 (181) | ···1··1111·111·1·11······111·1·11···11111·1····11·1·11··11·11·1111·1·····1··1·1·1····1······111·1··111·1111··1·····11·1··11·1··1·1111··1·1·1·11·1····1··11·1······11··1·1···1··1··11·1··111····11·1··1········1··1··11··1111·1··11·····1111····11··111·11·1·······11··1··11··1·1·1···1111··1···1····11·1·1·····1·1···1··1·11··1111····1········111··11·1··1·1111··1··1·11·1·1···1··1·1·1······11·1·1···1··1·11·1···111·····11··1···1·······1·· |
| out 16 (183) | ···1·1·111··1··11···11····11·11·1··1··1·11·····11·1·1·········1·1·111·1··1··1·1····1···1·····1111·11·····1···1··1··11··1·1·1111·11··11·11111·1111·1·111·111··1··1··1·····111······11··11·11····11·111··1···1··1·11·1·1··111··1·1···11···111·1···1·1··1··11········11··1··1···········1·1·1·111·1····11··1·1····1·1·1·11·1·······1·····1····1···11·1·1·1111·11··11·11·1·11·1111·111·1·11·1···1··1····111·····11···11·11·····11··1·11··1··1··1·1 |
| out 17 (173) | ····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·······111·11··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··111·1·1··111··1······111·1·1··1·····11111·····1··1······ |
| out 18 (151) | ····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··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··11·1·111····1·11··1···1·1·1···1··11··1·······1·····1··1·1 |
| out 19 (165) | ···1111··1··1·1·1····11···11·1111··········11·1111··1··1·1·1········1····11·1···1····1··1···11111·1····1111··1·111··1·11·1··111·1··11········1····11·111111··11·1········1·····1·111··11···1··1··1··11········1·11111····11·1··1····11··111·1··11···········1·1··111·1···1··1··1··········1·1··1··1·1··1·1·1···1·1·1·11·······1111····1··1·11···111·1··111·1··11········1····11·1111·11·1·1·1·······1·····1111···11···1···1··1····11·······1·1 |
| out 20 (165) | ···111···1······1·······111··11··1·11···111·1·····1····1·11·1·····11··11····1··11········1··11·11·11···111···1··1··1··11···1·11·1····1·11··1·1111·11··1111···111··1·····1·11·······11·11··11······11·1·1··11·11·1111·····1·····1·······11·1·1····111····111···1·······1·····1·1··1·······1·1·11·····1·11·····1·1···1·11·1·····111·····1····1···1·11···1·11·1····1·11···11·11111··111·1··1·11··1····1·11······11··11··11········1·1·1·1·11·11·1 |
| 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···1·111···1·····11·11····1··1111··1··11···11······1·1·1··11·1·····1·1·1··1···11····11·1·111··1·1·········11····1·1111·11···1·111·1·111··1·111··111·1··1·11·····1·1·······1··11·111···111111··1···1··1····1·1··1·1·11·1···1····111·1·····1··1·111····1···11·····11······1···1·1···111······11·11·11···1·1···11·1·1···1·1··············11···1·1111·11···1·11·1·11·11·1·111···1111···1·11····1·1······1···11·111····111·1·11··11·1··1·· |
| out 23 (189) | ·······111···11·11·········1·1···1·1·11111·11·1·1·1·1···11··1·11111·1·11····1··········111··1·11··1111··11···111·1·····1··1111···11··1··11·1··11··1·11111·······1·11··1···1111·1····111·1·11··11·1·1·1·1··11·11·1····1··11·11··11········111·····11·11·111··1·1··1·1··1··1···1···1···11111··111·····1·····11·1···1·1··1·1·11···11·····1·11··1·····1··1111···11··1··1·1·1··11·1·11111········1·11·1···1111·1···11·1·1·11···11·1···1·1·1·11·11·1 |
| 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 (183) | ···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··11·1111··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··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 (165) | ···11··111··1··1··1·111···1··111····1·11·11·1·111···1··1·1··1···1·1···1··1····1·1··1·1·11···1······1····1····1··11·11·11······1·11·1·1···1···1·11··1·1··1·1···1·1·11···1··1·1··1·11··1···111··111111·1·1···1·····11··1··111··1···1·111··1·1·1··1···1·1·1·11···1··111·····1··1····1·····1·1···1·1·····1·11111············1······1······1····11··1111······1·11·1·1····1··1··11·1·1··1··1···1·1·11·····1·1··111··1····111···1111·1·1·1·1··1····· |
| out 28 (167) | ····11··1····1···11111···1····11···1·1·111···11·1····1··1·····11111···1·········1··1···11·····111···1·1···1···111··11·11·111····111111··1··1·11·1·1111···1····11···1··1··11···11···1·1····1··111·1111·1··1········11····1··1····11111··1····1··1··1·1··111·····1·1·1······1··1·······11111···1·········11·11·····1·1·1····1·1····1······11·1···1111·111····111111··1···11·1·11111····1····11···1·1··11···11··1·1·····1·1··11·1·1·11·1········· |
| 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·····1111111·1111·1·1··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······1·1·11·1·1·1111···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 (183) | ···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···1111111··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······1·11··11·1·1111·1··1···1·111111···1111·1··1··········1 |
| out 35 (149) | ··11····1···1·11······1···1··1·111·11·11··1·1·11····1111·1·11·1·····1·1··11····11····1·1····1·1····11··1··1·····1···1·········1·1··1·1·1·1·········1····1·11·1111·11·····1·····1·11······111·1111·1·11·····1····11······1·1·11·······1··1·1····11111·1·1··1···1··11······1111··1·1···1······11·1··1···11·11······1······1·1···1··1·········1····1········1·1··1·1·1··1········1····1··111·111·11····1·····111·······1111··111··1··11····1····1 |
| out 36 (183) | ···1··1111···11··11··11··1···11··1·111·111·11···1····1·11·11··11·11···11····1···········1····1······11·1111··111······1··1·····1111··1·····1·1·11··1·1·11111·111······1·111·11···1·11···1·11··1111111··1··1··11··1··11··11·11···11··11·1··1·1····1111··111··1·1····1······1·1111··1··11·11···11·····1······1···1··········11··1111····1·11·······1··1·····1111··1······11··11·1·1·11·1111·11·····1·111·11··1·11····1·11···1111·1·11··1·1··11·· |
| out 37 (143) | ······1··1··11···1····1··11···1·····11··11····11··1····1·······1·1········1········1···1······1·1····1·1111··11111····1··111··111·1··1·11··1··111··11····11···1·······1·1···1··1·1·1·1·11··1··1····1··11···1··1·1···1····111····1····1·11···1······11···11·······11···1·····1·········1·1·········1·····1·1······1···1·····1··1111····1·11·11····1··111··111·1··1·11···1··111·11·····11··11······1·1···1··11·1·1··11··1···1······1··11··1··1·1 |
| out 38 (159) | ···1····1···11···1·······1···1·····111····111··111···1·11·11···11111··11····1··1···1····1····1··1··111··11····11···11·11·1·1···1··1··1··1·······1··1·1···111··111·····1·111·11·····111··1·11··1·11··1·····1··11··1······1·11····1······1··1·······111·····1·1·1···11·1····1·1111······1111·1·11·····1·1·1··1···1·····1··1·11···11····1··11·····1111·1·1···1··1··1··1········1·1·1····111··111····1·111·11····111···1·11···1·11····1····1··11·· |
| out 39 (191) | ······11·1··1····1111111·111·1·1······1··111·11·11·1·1111·11··111··1········1·1·1··1·1··1·········1·1·11···1···111··1·1··11···1·····1·11·1·1·1·11·1····1·111·1111·11·11·1·1111·1····1·1·1·1···111·1·11·····1·11·1···11···11·····11111111111····1·····11··11·1··1·1·1·1·1··111111·····111···1········11·111·1··········1···1·1·1····1·····1·11···11··11···1·····1·11··1·11··111····1··1111·111·1111·1·1111·1···1··1·1·1····111··1··11····1·11·1 |
| 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··111·1··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 (167) | ·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··11·1111···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····1·111··1·1··1·11··111··1·1·1111····1···1··1·1······1·1 |
| out 42 (149) | ···1·1······11·1·1········1·1·1··1·1·1·····11·11········11··1··1·1111··1··1···111··1···1·1··11··1···11··1·····11·1·11·11·11··1111·1··········1··1······1·11··1····1···1··11·1··1···11··1111···1···1·11····1··1···1·1······11·1··1·······1···1····11·1·······1·1··11··········1···1····1·11·11·1···1··1111·1··1·1·····1····11···1········11··1··1111·11··1111·1··········1···1·····1··11·1·····1··1··11·1··1··11···1111····1····1··11···1··1··· |
| out 43 (173) | ···1·111·1···11·1·1·1····1·1·1111··1·1···1111··1··1····111·11··111··1·1·········1··1·1·111··1··1··11·1··1·1··11····1··1···1111·11·1111········111·1···1·1·1·····1·1···1··1·11··1·····1111········11111·1···1··1··1·111···1·11··1·1·1···1·11·1··11·1·1····11·1·1···1···1·····11·1·1····111···11·········11111·1·····1··1·1··1···1·11···1·1······1·1···1111·11·1111·········1111···1·1··1·····1·1··1··1·11··1····1·111·········1·1·111·1··1··1·· |
| out 44 (63) | ····1·1···········1·1··············1·1········1·1····1·1········1·1·····················11·········11···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··············11················1·1·········1·1······11··········1·1·······················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 (175) | 1··1·1·1·1··1··1····111···11··1·1··11·1·11·1····1·1·1···1·······1·111····11·1·1·1··1···1·1···11·1·1·····11···1·11··11·11·1··111·111·11·111·1·1111···111··1···1··1········11······111··1··11·····1·111·11······1·11·1·1···11··1·····111··11··1···1·11·1··11··1······1··1··1···1·········1·1·11··1··1·11·11·1··1·1·1···11········11·····1··1·1···1111·1··111·111·11·11·1·11·111··111···1··1···1·······11·····111···1··11······1··1·11·11·····1·1 |
| out 47 (165) | ···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·······11···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··111··1····11·11·1·1······1·1···11···1·1·····1111·11····· |
| out 48 (159) | ····1····1··11···11·1·1··11··1······11··1111··11··1····11·1····1·1··1·1···1·1·1····1···1···1·11·1····1·1·1···11111··1····111···1··1··1·11··1·1·11··11····11···11······1·1···11···1·1·1··11·1··1····11··1···1··1·1·1······111····11·1·1·11·1········11···111·1····11···1·····111·······1·1···11····1·11··1·1····1·1···1·····1··1·1·····1·11·11···1···111···1··1··1·11···11··11·11·····11···11·····1·1···11··1·1·1···11·1···1······11··1··1··1·1 |
| out 49 (183) | ···1111111··1··11·1··1····11·11·1···1·11·1·······1··111···11··1·11····1··1··1·1····1···111···1111·1·1···111··1··1··1··11·1·1111·11··11···1···1111·1···11·11111·1···1·······111····11··11·11····111·11··1···1·····11111··111··1·1·1··1···111·1···1··1·1·1·1···········1···111··11·····1·11····1·1····11··1·11·1·1·1·1·11···1····111····1····1···1·11·1·1111·11··11····1··1·1111···11··1111··1···1······111···11···11·11·····111···11··1··1····· |
| out 50 (175) | ···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··111·1·11···11·11····11·11·11···111··1····111·1··11·11·1···1·11·······1111···111111·1·1···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····11·1·1··11······11··11···11·11·11···111···1····1111··11·1·1·1···1·11······1111··11111·1·1·1···11·1··1··1··1····1··1 |
| out 51 (181) | ····111·1·····1·1·1··1····11·1·11······1·111···111·····11111··1·1···1·11·11·1··11···11·1····11·11··11·1··1111··1·1··1·1·····1·11··111·111·········1111·11··1·1111111·····1·1·1····1····11·1····11·1111····11····1·111···1···1··1·1··1···111····11······1·11·1·····11·1······1111·····1·1····1111··1·1·11·11····1···1·1··1·1·1···11·11····1··1···11·····1·11··111·111·········1111·11···11·111111····1·1·1···1·····11·1·····11··1·111···11····1 |
| out 52 (165) | ····111·····1··111·······111··11·1·1······1···1········1·11·1···1··11··1····1··11····1·11···11·11·11····111····111····11·1·111··1··1·1·1····1111··1···11·1···111··1········1·1·1···11·11··11··1·11·1·1·1··11·11·1·111·····1··1·11······111··1··1·11·······1······1··········1·1··1·····1···11·1·····1·11·111···1···1·11·1······111·······1·11····11·1·111··1··1·1·1·····1·11·1···11··1··1·11··1·······1·1·1··11··11··11···1·11···1·1·1·11·11·1 |
| out 53 (165) | ·····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·····11111···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··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···11·1·1·1··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 (149) | ···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·······11···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·····11·11··1··1·11·1·1······1·1···11···1·1······11···1··1·· |
| out 56 (181) | ···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··11111····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··111·1·1·11·111·1······1··1·1·1111·1····1·····1······1···11·1··· |
| out 57 (175) | ···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··11·1111··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··111111·11·1·11··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 (151) | ···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···1·1·1·11··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··1111·11·····1···1·11··1·1·1··11··1···1······1··11··1··1·1 |
| out 60 (173) | ····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····111111·······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··1·11·1·1·11····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···11·1·111···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 (173) | ····1·111·1·1·1·1·1···1··1·1·11··1··1·11·1·11·111···11·111····1···1·1·1···1·1···1··1·····1··1·111·1·1·11··1·1·········1··1··1111111····1··········11·111·11···1·1·11·1··1·11·····1·111111·1···11·1·1·11······1····1·11··1·1·1··1·1···1·1·11·1····1·1·1·1·1··1·1··111·····11·11·······1···1··11····1·1··11····1···1·1·11···1·1·1··1··1············1··1··1111111····1··········11·111··11···1·1·111··1·11····1·111·111·1····11·1···1·11·····1··· |
| 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 (157) | ········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·······1·1··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···1·11·1·11······1·1·1··1······1·1···1111····11····1·111········ |
| out 65 (183) | ····11·111··1·111····1····11·11·1·····1111·····1····11····1···1·1··1··1··1··1·1····1····1····1111·111··111···1·····11·11·1·1111·11··11··11·1·1111·1·1·1··111·1·11··1·····1·1·1····11··11·11····1·1111··1··11··1···11·1··111·11·1····1···111·1···1····1·111········1······11···1······1·1···1·1·1····11··1··1···1·1·1111·1·1···111·····1········1111·1·1111·11··11··1·1·11·1111·1·1···1111··11··1····1·1·1···11···11·11·····1·1·1·11··1·11··1·· |
| out 66 (157) | ····11··11··11·11·········11···11··11··11········11··1·1·1·1··11·11····1·1··1·1······1·1·1··11··1·111·1111··11·········1·11·1··1·1·11········11····1··1·······1·1·11······11······1111·1111····11···11····11·1··1·11····1111·1·1········11·····11·11···11············11···1·1··1·····11·11····11····11···11··111·····11·1·1·1·111···1·1···········1·11·1··1·1·11········1·1···1··1········1·1·11·····11·····1111··1111·····11·····11···11·1··1 |
| out 67 (175) | ···1··1·1····1··1·1···1··111·11·11·1·1·11······11·11······11··1111·1··11·1··1······1·1···1···1·11··1·····11···11·······1·1·11·111···1···1··1·1····1111·1·1···1111··1··1·11·111·1·1111··11······11···1·1···11·1··11··1···1··1···1·1···1·1111·1···111·1··11·········11··11······11·····1111··1·111····1···11···1·1···1·1··1·······11······11········1·1·11·111···1···1···11····1111·1·11··1·111··1·1·11·111·11111···11·······11·····1·1··11·1··1 |
| out 68 (191) | ····11···1··1·1··111··11·····1·111·······11·11·1·111·1111·11··111·111····11············111···11····11·1·11111·11·······1···1111··1····1····1··111·1111111·11··11···1·1··11·111·1··1111·111·1··11·····11····1·1····11·····11·1···111··11···1····111·······11···11··1··111··111111·····111·1·11··1··1·······1111·1·1······1·1·1··111·11···11········1···1111··1····1·····1··1111111111··11··11···11··11·111·1·1111··111·1···11·······11···1·1··· |
| out 69 (149) | ···1····11···1·111·····1·11···11·1··111·····1··1·11····111·····1·111·····1····1·1··1····1···111·1······111··111·······1··111···11111·····1·····1·····1·1·1···1····11··1···11···1···1····111····111···111······1·11······11·1·1·11·····111···1··1·1·111········1···1··11·····11········1·11·1···1·····1·11··1···1·1···1········111···1·1·1········1··111···11111······1·····1····1·1··1··1·····11·1···11···1··1·····111·····111·····111···1·1·1 |
| out 70 (173) | ···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··1·111·11····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··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····1111·1···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 (183) | ·····1111·····11·11·1·1······1··11·11·1··111···111111··11···1···1·111·1··1··1·111··1·1·1·1···1111·11····111·1······1·····1··111···1·1····1····1·1·1··111111··1··1··1·····11·1····111··11·11····11·111·1·······111··111··1···11··11·1·1····1·····1111·1···11·1·····11·111·1··11···1·····1·1·111·1····1111111··1·1·1·1·11·1······111··1··········1····1··111···1·1·····1····1·11··1111·11·1···1··1····11·1···111··111·11·····11··1·11·1······111 |
| out 73 (165) | ···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··1·1·111·1·1·1··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·····1·11··1·····1··1·1·1111·1·1···111····1········1····1··1·1 |
| out 74 (157) | ···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··1·111··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····1·1··11··1·1··1·11··1·1·11·1··1··1···11·······11·11·1··1 |
| out 75 (173) | ···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··11·1··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··1·····11·1···1·1··1·11·1···111·····111·····1·········1 |
| out 76 (111) | ······11·1··1·1·1·1·11····1··11··1··1···111····1·1··1···1·······1··1···········1···1·········1·1·····1·11·1··1·1···11··1···1····11······1··1·111··1·1··1·····1··1··········1···1·······1···1·······1···1············11···11·1··1·1·11···1·1·1·1··1·1····111·······1··1···1···1·········1···1··········1·1······1···1·······1··11·1····1··1·····11·1···1····11······1···11·11·1·1··1·····1···1·········1···1·······1···1··········1···1········ |
| out 77 (173) | ···111···1······1·····1···11···1···11···111·1·····1····1·11·1···1··11··1····1··11····1·11···11·11·11···111···1··1··1··11·11111·····1···11··1·1111·11··1111···111··1········1·1·1···11·11··11··1·11·1·1·1··11·11·1111·····1·····1·····1··11·····1··11····111···1·······1·····1·1··1·····1···11·1·····1·11·111···1···1·11·1·····111·····1····1···1·11111111·····1···11···11·11111··111·1··1·11··1·······1·1·1··11··11··11···1·11···1·1·1·11·11·1 |
| out 78 (157) | ······111···1·1··1·······11··1·1·1·1··111·1·1·11····11···11·1·1·1·····11·1····111··1·1···1··1·1····11··1··1·····11·11··1···1··1····1···111·1········1··1··11·1111·11····11···1·1··1·1····1·1··11····11····1··11·1···11··1·1·1···1······11·1··1·1·11··1·11·1···1··11······11···1··1···1·1·····111·····11111···1···1······1·1···1··1·········11··11·1···1··1····1···11·1·1·······1··1···111·111·11···11···1·1·1·1·····1·1···11······11···1··11·1 |
| out 79 (173) | ···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··11·11····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···11·1111···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····11·11·11·11·1·1·1····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 (174) | ···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··111·1·1111·····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··1·1·1·11··11·1··1·····1·1·111·1··1111······11·····11···1·111· |
| check 83 (168) | ···1··1111···111·1···111·1·1··1·11··11·1·11·1···11·11···1··1···1···1···1····1·111··1·····1····1·1····1··1·11·11·····1····11·1·1·111·1··111·····1·····1··11···1···1·1··1·11···1···111·····1····1·11·11··1···1·11111··11··11·111··1···1111·1··1···11·11··1·11···1····1·1·1·1···1·1······1····1··1·····11111····1···1···1·····1···1·1·1··1·1·······1···11·1·1·111·1··11·1·····1····1··1·1··1····1·1·1·11···1··111······1·····1·11···11··1··1·1111 |
| check 84 (176) | ···1·11··1··11·1··11···1·1·1··1·11·111·11·1···1···1111·1····1·11··1·1·1··1····1·1··1···1·····1··1····1·1··1·111·1·1·1·····1·111111··1··11··1···1·······111·1·11·······1·11···111······111111······1·1·11··11·1·111·11····111·1···11···11·1··1···11111··11·1······1····11·11·1····1···11··1··11·1·····1·11·1····1·····1·····1··1··1··1·1·1··1·1··1····1·111111··1··11···1···1······11·1·11·1······1·11···111······111111········1··1·11·11·1·11 |
| check 85 (152) | ·······111··1··1······1··········1······1·1···1··11··1······1····111···1·11···1·1··1···111·····1····1·11··1·11·1·1·1··11···1·1·1·1··1··11··1·1·1··1·1··1·1···1·11··1·····11····1·11···1·1111·111111····1··11··1······1··111··1·······1···········1······1·1······1···11···1······1······11·1··11··1··1·11·11·1·····1······1·1·1··1··1·1··1··1··1·11···1·1·1·1··1··11···11··1·1·1··1··1··1··11··1····11····111····1·11111··1111·1·····1·11··1·· |
| check 86 (184) | ····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·····111·11111·····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··1·11··1·11·111·11····111··11111······1···1·1·1····11·1 |
| check 87 (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 88 (160) | ····11······111···1··111···1·11·······11···11···11····11······11··1···11··1···111··1·1·1·····11···11···11··1111·11··1·11·11111111····11··1················11·11····1··1·1··1········1·11···1···1··11111···11·11···11······111····1··111··11·1········1·1····1·1····1·1·····11········11··1···11···1··111111····1·1····1·1·····11···11·1·1··11···111·11111111····11···1················111·1····1·1·1··1·······1··11···1····1···1·1111··11·11·· |
| check 89 (142) | ·······1·1··11··1··11····111····1····1···1··11·11·1···1·1111···1······1··1··1···1··1·1·11···11·1··1··1·1··1··1111·········1·1111···1···1·····1·······11·1··1···11·····1··11·11·1··1··111·11······1·····1···1·········1···111···1··11···111······1···1····1····11··11··1····1·111······1······1·1····1··11111···1···1··1····1··1··1····1·11·1·········1·1111···1···1·····1·······11·1···1···11····1··11·11·1·1··1·11·11·······1·······1··1····· |
| check 90 (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 91 (184) | ···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···111·11111··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····1·1111·1·111111·1···1111··111··11111···1·11·······1······1· |
| check 92 (256) | 11111·111·1111······111·1·1·1··1··111··11·111··1·11····11111·111··1·11·11··1·111·11·1·1··1111·11·11·1·1··111·1·11··111111··1··111·11·····1111··1111·11·1··1·1··1·1·111·11·1·1···1·11···1··11111··11··11111··1·1·1··1··11·1··1111111···11·111111·11··111··1·1·1·111·11··11111····11111··11·11·1·111111··111111·111·1·11·111·1·111··1·11·11·1·111····111·11···1··111111·1·111···1··1·111·1111·1·1··11·1·1·1111··1111·11···11·11·1·111···11111·1· |
| check 93 (214) | ·1·1···11··1·11·11······1··111········111111··1·1·1·11·11··1·111111····11··111···1·····111·11·1·1··111··11··11·1·1··1·11·11·11····1·····11·1·111····1111·1····1···111·····1111·1·1··1·1·1··11··111·111·11·1·11·····1···111··11··11·1·1··1111·1·1·11·1111·1····1·11111···11···1···1·1·1·1·11·111·1·1·1·1·11·11111···1··1····11·11··1·····111···1···11·111··1·111·1·11111····111··1·11···11···1··1·11·11·1·····111·····11·1·11·11·11·111111·11·1 |
| check 94 (206) | ··1··1111····11·····111·111·11111··11··11······11········1·1··11····11·1·111···1··1···1·1····1·1111·1··1··1··11·1···111·1··1··11···11·····11·11··1111··11···11·····11·11·········1·111··111··11··1··1····111111·11·1·····11·1·11··1·1111111··1·1·11·1······11··11·1·1··11··11·1···11·····11·111·1·11·1··1·11·11···1··1···1···1····1··1··1111·11·1···1·1111111·1·1··11···11····11111111·····11····11··11··1111·1111·1····1·1111·11·111·1111111· |
| check 95 (214) | ···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··11·11···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··111·11·11·1··11····1·111····1111··111···1·1·11111·1·1··11· |
| check 96 (222) | ·····111·111··1······1··11·11111··1·11·····1······1····11111·1········111111···11··11111·1··111··1····111111··111··11··11·1·11111111·1··111···111····11·1··1··11·1··1111····11·111·1·11·1·····11·1···111····1······111111·111········11·1·1·1··1··1··1111···1····11111·11···11111111111······1··11·1··111··11·11·1··1111111·1·1111··1111··11···11··11·1··111111·111·1·11··111·11··1·11·1··11··11··1····11·1·1·1·1··1·····1··1·111··111·1111111 |
| check 97 (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 98 (216) | ······111···1···1111·1·1··11···11·111·111··11··11···11·1···1····11·11··1··1·111··111111111111111111·11·1···1···11··11·1····11·1··1·1·1·1·1111···11111······1···1·1·1·····1·11111··1··1··111·1·1·111·11··11111···1···11··1·1····1111·1·1·1111111··1··1·1··111·1·111··1111111·1··1·······11··11·1···1···11····1·1·1·1·1··111·1··1····1·····1·1···111····11··11·1·1·1·11·1·1111····111111·1···1·1·1····1·11111·1··1··1···1111·1··1·11··111··1111· |
| check 99 (232) | ····1·11·1··11·1··11·1·1·111·111····1·11···111·111··1111·11111·1··1··11·11·111··111·111·11111·11·11·111111·11·1····1·····11111··1··11·1·11·····11·11···11···1····1··1··1·11·11·111·1····1··11·11·1·1111111111·1·1·1·11···111·1···11·1·11111·1··1···1·1·1····1·11··11·1·······1··1·1111·11·111·1·1111·11·1·1·1·111·1·11·111·11·111··11···1······1····11111··1··11·1·1·1·····1111···11··1111111·111111··1··1··1·11111·11·111··1·111·····1··11·1· |
| check 100 (214) | ···1·11·11··1··1··1·11·1···1·111···111···11·1···111·111111·11···1·1···1··1··1·11·········1··1···1·1·1·111···1······1·11·1·1111111·1·1·····1·1··1·1·1·1···11·11·11··11··1111·11111·1·1111111111111···11·11111111··1·11···111··1···1·11·1··11·1··1··111····11···1····1·11··11111·1·1·····1·1···1·1····111······1·······11···11·1··1111·1111111111·1·111·······1·1·11111111111·11·1·1111··1·11··11·111···1····1·1··1·······11···11111··1·1··1··11 |
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 n430Noisy T states per run.
outputs k80
distance d4Exact, proved and witnessed here.
error coefficient A_{4}7,262Faults 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 N101
checks r21
V_{\mathrm{ex}}80T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.2131Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.2131Overhead 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 89 single-wire gates and 1128 \mathrm{CZ} gates: \mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{Z} on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{Z} on output 6, \mathrm{Z} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{Z} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{Z} on output 17, \mathrm{S} on output 18, \mathrm{Z} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23 and 1193 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.
All 1217 correction gates
\mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{Z} on output 3, \mathrm{Z} on output 4, \mathrm{S} on output 5, \mathrm{Z} on output 6, \mathrm{Z} on output 7, \mathrm{S} on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{Z} on output 11, \mathrm{Z} on output 12, \mathrm{S} on output 13, \mathrm{Z} on output 14, \mathrm{Z} on output 15, \mathrm{S} on output 16, \mathrm{Z} on output 17, \mathrm{S} on output 18, \mathrm{Z} on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{S} on output 22, \mathrm{Z} on output 23, \mathrm{Z} on output 24, \mathrm{S} on output 25, \mathrm{S} on output 26, \mathrm{Z} on output 27, \mathrm{S} 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{S} on output 34, \mathrm{Z} on output 35, \mathrm{S} on output 36, \mathrm{S} on output 37, \mathrm{S} on output 38, \mathrm{S} on output 39, \mathrm{S} on output 40, \mathrm{S} on output 41, \mathrm{Z} on output 42, \mathrm{Z} on output 43, \mathrm{S} on output 44, \mathrm{S} on output 45, \mathrm{S} on output 46, \mathrm{Z} on output 47, \mathrm{S} on output 48, \mathrm{S} on output 49, \mathrm{S} on output 50, \mathrm{Z} on output 51, \mathrm{Z} on output 52, \mathrm{Z} on output 53, \mathrm{S} on output 54, \mathrm{Z} on output 55, \mathrm{Z} on output 56, \mathrm{S} on output 57, \mathrm{S} on output 58, \mathrm{S} on output 59, \mathrm{Z} on output 60, \mathrm{Z} on output 61, \mathrm{Z} on output 62, \mathrm{S} on output 63, \mathrm{Z} on output 64, \mathrm{S} on output 65, \mathrm{Z} on output 66, \mathrm{S} on output 67, \mathrm{S} on output 68, \mathrm{Z} on output 69, \mathrm{Z} on output 70, \mathrm{S} on output 71, \mathrm{S} on output 72, \mathrm{Z} on output 73, \mathrm{Z} on output 74, \mathrm{Z} on output 75, \mathrm{S} on output 76, \mathrm{Z} on output 77, \mathrm{Z} on output 78, \mathrm{Z} on output 79, \mathrm{S} on check 80, \mathrm{S} on check 81, \mathrm{S} on check 82, \mathrm{S} on check 89, \mathrm{S} on check 93, \mathrm{S} on check 94, \mathrm{S} on check 95, \mathrm{S} on check 96, \mathrm{S} on check 100, \mathrm{CZ} on output 3, output 4, \mathrm{CZ} on output 3, output 6, \mathrm{CZ} on output 3, output 7, \mathrm{CZ} on output 3, output 9, \mathrm{CZ} on output 3, output 10, \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 15, \mathrm{CZ} on output 3, output 17, \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 23, \mathrm{CZ} on output 3, output 24, \mathrm{CZ} on output 3, output 27, \mathrm{CZ} on output 3, output 35, \mathrm{CZ} on output 3, output 42, \mathrm{CZ} on output 3, output 43, \mathrm{CZ} on output 3, output 47, \mathrm{CZ} on output 3, output 51, \mathrm{CZ} on output 3, output 52, \mathrm{CZ} on output 3, output 53, \mathrm{CZ} on output 3, output 55, \mathrm{CZ} on output 3, output 56, \mathrm{CZ} on output 3, output 60, \mathrm{CZ} on output 3, output 61, \mathrm{CZ} on output 3, output 62, \mathrm{CZ} on output 3, output 64, \mathrm{CZ} on output 3, output 66, \mathrm{CZ} on output 3, output 69, \mathrm{CZ} on output 3, output 70, \mathrm{CZ} on output 3, output 73, \mathrm{CZ} on output 3, output 74, \mathrm{CZ} on output 3, output 75, \mathrm{CZ} on output 3, output 77, \mathrm{CZ} on output 3, output 78, \mathrm{CZ} on output 3, output 79, \mathrm{CZ} on output 3, check 80, \mathrm{CZ} on output 3, check 81, \mathrm{CZ} on output 3, check 82, \mathrm{CZ} on output 3, check 89, \mathrm{CZ} on output 3, check 93, \mathrm{CZ} on output 3, check 94, \mathrm{CZ} on output 3, check 95, \mathrm{CZ} on output 3, check 96, \mathrm{CZ} on output 3, check 100, \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 89, \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 96, \mathrm{CZ} on output 4, check 100, \mathrm{CZ} on output 6, output 7, \mathrm{CZ} on output 6, output 9, \mathrm{CZ} on output 6, output 10, \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 15, \mathrm{CZ} on output 6, output 17, \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 23, \mathrm{CZ} on output 6, output 24, \mathrm{CZ} on output 6, output 27, \mathrm{CZ} on output 6, output 35, \mathrm{CZ} on output 6, output 42, \mathrm{CZ} on output 6, output 43, \mathrm{CZ} on output 6, output 47, \mathrm{CZ} on output 6, output 51, \mathrm{CZ} on output 6, output 52, \mathrm{CZ} on output 6, output 53, \mathrm{CZ} on output 6, output 55, \mathrm{CZ} on output 6, output 56, \mathrm{CZ} on output 6, output 60, \mathrm{CZ} on output 6, output 61, \mathrm{CZ} on output 6, output 62, \mathrm{CZ} on output 6, output 64, \mathrm{CZ} on output 6, output 66, \mathrm{CZ} on output 6, output 69, \mathrm{CZ} on output 6, output 70, \mathrm{CZ} on output 6, output 73, \mathrm{CZ} on output 6, output 74, \mathrm{CZ} on output 6, output 75, \mathrm{CZ} on output 6, output 77, \mathrm{CZ} on output 6, output 78, \mathrm{CZ} on output 6, output 79, \mathrm{CZ} on output 6, check 80, \mathrm{CZ} on output 6, check 81, \mathrm{CZ} on output 6, check 82, \mathrm{CZ} on output 6, check 89, \mathrm{CZ} on output 6, check 93, \mathrm{CZ} on output 6, check 94, \mathrm{CZ} on output 6, check 95, \mathrm{CZ} on output 6, check 96, \mathrm{CZ} on output 6, check 100, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, output 10, \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 15, \mathrm{CZ} on output 7, output 17, \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 23, \mathrm{CZ} on output 7, output 24, \mathrm{CZ} on output 7, output 27, \mathrm{CZ} on output 7, output 35, \mathrm{CZ} on output 7, output 42, \mathrm{CZ} on output 7, output 43, \mathrm{CZ} on output 7, output 47, \mathrm{CZ} on output 7, output 51, \mathrm{CZ} on output 7, output 52, \mathrm{CZ} on output 7, output 53, \mathrm{CZ} on output 7, output 55, \mathrm{CZ} on output 7, output 56, \mathrm{CZ} on output 7, output 60, \mathrm{CZ} on output 7, output 61, \mathrm{CZ} on output 7, output 62, \mathrm{CZ} on output 7, output 64, \mathrm{CZ} on output 7, output 66, \mathrm{CZ} on output 7, output 69, \mathrm{CZ} on output 7, output 70, \mathrm{CZ} on output 7, output 73, \mathrm{CZ} on output 7, output 74, \mathrm{CZ} on output 7, output 75, \mathrm{CZ} on output 7, output 77, \mathrm{CZ} on output 7, output 78, \mathrm{CZ} on output 7, output 79, \mathrm{CZ} on output 7, check 80, \mathrm{CZ} on output 7, check 81, \mathrm{CZ} on output 7, check 82, \mathrm{CZ} on output 7, check 89, \mathrm{CZ} on output 7, check 93, \mathrm{CZ} on output 7, check 94, \mathrm{CZ} on output 7, check 95, \mathrm{CZ} on output 7, check 96, \mathrm{CZ} on output 7, check 100, \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 89, \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 96, \mathrm{CZ} on output 9, check 100, \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 15, \mathrm{CZ} on output 10, output 17, \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 23, \mathrm{CZ} on output 10, output 24, \mathrm{CZ} on output 10, output 27, \mathrm{CZ} on output 10, output 35, \mathrm{CZ} on output 10, output 42, \mathrm{CZ} on output 10, output 43, \mathrm{CZ} on output 10, output 47, \mathrm{CZ} on output 10, output 51, \mathrm{CZ} on output 10, output 52, \mathrm{CZ} on output 10, output 53, \mathrm{CZ} on output 10, output 55, \mathrm{CZ} on output 10, output 56, \mathrm{CZ} on output 10, output 60, \mathrm{CZ} on output 10, output 61, \mathrm{CZ} on output 10, output 62, \mathrm{CZ} on output 10, output 64, \mathrm{CZ} on output 10, output 66, \mathrm{CZ} on output 10, output 69, \mathrm{CZ} on output 10, output 70, \mathrm{CZ} on output 10, output 73, \mathrm{CZ} on output 10, output 74, \mathrm{CZ} on output 10, output 75, \mathrm{CZ} on output 10, output 77, \mathrm{CZ} on output 10, output 78, \mathrm{CZ} on output 10, output 79, \mathrm{CZ} on output 10, check 80, \mathrm{CZ} on output 10, check 81, \mathrm{CZ} on output 10, check 82, \mathrm{CZ} on output 10, check 89, \mathrm{CZ} on output 10, check 93, \mathrm{CZ} on output 10, check 94, \mathrm{CZ} on output 10, check 95, \mathrm{CZ} on output 10, check 96, \mathrm{CZ} on output 10, check 100, \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 89, \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 96, \mathrm{CZ} on output 11, check 100, \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 89, \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 96, \mathrm{CZ} on output 12, check 100, \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 89, \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 96, \mathrm{CZ} on output 14, check 100, \mathrm{CZ} on output 15, output 17, \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 23, \mathrm{CZ} on output 15, output 24, \mathrm{CZ} on output 15, output 27, \mathrm{CZ} on output 15, output 35, \mathrm{CZ} on output 15, output 42, \mathrm{CZ} on output 15, output 43, \mathrm{CZ} on output 15, output 47, \mathrm{CZ} on output 15, output 51, \mathrm{CZ} on output 15, output 52, \mathrm{CZ} on output 15, output 53, \mathrm{CZ} on output 15, output 55, \mathrm{CZ} on output 15, output 56, \mathrm{CZ} on output 15, output 60, \mathrm{CZ} on output 15, output 61, \mathrm{CZ} on output 15, output 62, \mathrm{CZ} on output 15, output 64, \mathrm{CZ} on output 15, output 66, \mathrm{CZ} on output 15, output 69, \mathrm{CZ} on output 15, output 70, \mathrm{CZ} on output 15, output 73, \mathrm{CZ} on output 15, output 74, \mathrm{CZ} on output 15, output 75, \mathrm{CZ} on output 15, output 77, \mathrm{CZ} on output 15, output 78, \mathrm{CZ} on output 15, output 79, \mathrm{CZ} on output 15, check 80, \mathrm{CZ} on output 15, check 81, \mathrm{CZ} on output 15, check 82, \mathrm{CZ} on output 15, check 89, \mathrm{CZ} on output 15, check 93, \mathrm{CZ} on output 15, check 94, \mathrm{CZ} on output 15, check 95, \mathrm{CZ} on output 15, check 96, \mathrm{CZ} on output 15, check 100, \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 23, \mathrm{CZ} on output 17, output 24, \mathrm{CZ} on output 17, output 27, \mathrm{CZ} on output 17, output 35, \mathrm{CZ} on output 17, output 42, \mathrm{CZ} on output 17, output 43, \mathrm{CZ} on output 17, output 47, \mathrm{CZ} on output 17, output 51, \mathrm{CZ} on output 17, output 52, \mathrm{CZ} on output 17, output 53, \mathrm{CZ} on output 17, output 55, \mathrm{CZ} on output 17, output 56, \mathrm{CZ} on output 17, output 60, \mathrm{CZ} on output 17, output 61, \mathrm{CZ} on output 17, output 62, \mathrm{CZ} on output 17, output 64, \mathrm{CZ} on output 17, output 66, \mathrm{CZ} on output 17, output 69, \mathrm{CZ} on output 17, output 70, \mathrm{CZ} on output 17, output 73, \mathrm{CZ} on output 17, output 74, \mathrm{CZ} on output 17, output 75, \mathrm{CZ} on output 17, output 77, \mathrm{CZ} on output 17, output 78, \mathrm{CZ} on output 17, output 79, \mathrm{CZ} on output 17, check 80, \mathrm{CZ} on output 17, check 81, \mathrm{CZ} on output 17, check 82, \mathrm{CZ} on output 17, check 89, \mathrm{CZ} on output 17, check 93, \mathrm{CZ} on output 17, check 94, \mathrm{CZ} on output 17, check 95, \mathrm{CZ} on output 17, check 96, \mathrm{CZ} on output 17, check 100, \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 89, \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 96, \mathrm{CZ} on output 19, check 100, \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 89, \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 96, \mathrm{CZ} on output 20, check 100, \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 89, \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 96, \mathrm{CZ} on output 21, check 100, \mathrm{CZ} on output 23, output 24, \mathrm{CZ} on output 23, output 27, \mathrm{CZ} on output 23, output 35, \mathrm{CZ} on output 23, output 42, \mathrm{CZ} on output 23, output 43, \mathrm{CZ} on output 23, output 47, \mathrm{CZ} on output 23, output 51, \mathrm{CZ} on output 23, output 52, \mathrm{CZ} on output 23, output 53, \mathrm{CZ} on output 23, output 55, \mathrm{CZ} on output 23, output 56, \mathrm{CZ} on output 23, output 60, \mathrm{CZ} on output 23, output 61, \mathrm{CZ} on output 23, output 62, \mathrm{CZ} on output 23, output 64, \mathrm{CZ} on output 23, output 66, \mathrm{CZ} on output 23, output 69, \mathrm{CZ} on output 23, output 70, \mathrm{CZ} on output 23, output 73, \mathrm{CZ} on output 23, output 74, \mathrm{CZ} on output 23, output 75, \mathrm{CZ} on output 23, output 77, \mathrm{CZ} on output 23, output 78, \mathrm{CZ} on output 23, output 79, \mathrm{CZ} on output 23, check 80, \mathrm{CZ} on output 23, check 81, \mathrm{CZ} on output 23, check 82, \mathrm{CZ} on output 23, check 89, \mathrm{CZ} on output 23, check 93, \mathrm{CZ} on output 23, check 94, \mathrm{CZ} on output 23, check 95, \mathrm{CZ} on output 23, check 96, \mathrm{CZ} on output 23, check 100, \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 89, \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 96, \mathrm{CZ} on output 24, check 100, \mathrm{CZ} on output 27, output 35, \mathrm{CZ} on output 27, output 42, \mathrm{CZ} on output 27, output 43, \mathrm{CZ} on output 27, output 47, \mathrm{CZ} on output 27, output 51, \mathrm{CZ} on output 27, output 52, \mathrm{CZ} on output 27, output 53, \mathrm{CZ} on output 27, output 55, \mathrm{CZ} on output 27, output 56, \mathrm{CZ} on output 27, output 60, \mathrm{CZ} on output 27, output 61, \mathrm{CZ} on output 27, output 62, \mathrm{CZ} on output 27, output 64, \mathrm{CZ} on output 27, output 66, \mathrm{CZ} on output 27, output 69, \mathrm{CZ} on output 27, output 70, \mathrm{CZ} on output 27, output 73, \mathrm{CZ} on output 27, output 74, \mathrm{CZ} on output 27, output 75, \mathrm{CZ} on output 27, output 77, \mathrm{CZ} on output 27, output 78, \mathrm{CZ} on output 27, output 79, \mathrm{CZ} on output 27, check 80, \mathrm{CZ} on output 27, check 81, \mathrm{CZ} on output 27, check 82, \mathrm{CZ} on output 27, check 89, \mathrm{CZ} on output 27, check 93, \mathrm{CZ} on output 27, check 94, \mathrm{CZ} on output 27, check 95, \mathrm{CZ} on output 27, check 96, \mathrm{CZ} on output 27, check 100, \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 89, \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 96, \mathrm{CZ} on output 35, check 100, \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 89, \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 96, \mathrm{CZ} on output 42, check 100, \mathrm{CZ} on output 43, output 47, \mathrm{CZ} on output 43, output 51, \mathrm{CZ} on output 43, output 52, \mathrm{CZ} on output 43, output 53, \mathrm{CZ} on output 43, output 55, \mathrm{CZ} on output 43, output 56, \mathrm{CZ} on output 43, output 60, \mathrm{CZ} on output 43, output 61, \mathrm{CZ} on output 43, output 62, \mathrm{CZ} on output 43, output 64, \mathrm{CZ} on output 43, output 66, \mathrm{CZ} on output 43, output 69, \mathrm{CZ} on output 43, output 70, \mathrm{CZ} on output 43, output 73, \mathrm{CZ} on output 43, output 74, \mathrm{CZ} on output 43, output 75, \mathrm{CZ} on output 43, output 77, \mathrm{CZ} on output 43, output 78, \mathrm{CZ} on output 43, output 79, \mathrm{CZ} on output 43, check 80, \mathrm{CZ} on output 43, check 81, \mathrm{CZ} on output 43, check 82, \mathrm{CZ} on output 43, check 89, \mathrm{CZ} on output 43, check 93, \mathrm{CZ} on output 43, check 94, \mathrm{CZ} on output 43, check 95, \mathrm{CZ} on output 43, check 96, \mathrm{CZ} on output 43, check 100, \mathrm{CZ} on output 47, output 51, \mathrm{CZ} on output 47, output 52, \mathrm{CZ} on output 47, output 53, \mathrm{CZ} on output 47, output 55, \mathrm{CZ} on output 47, output 56, \mathrm{CZ} on output 47, output 60, \mathrm{CZ} on output 47, output 61, \mathrm{CZ} on output 47, output 62, \mathrm{CZ} on output 47, output 64, \mathrm{CZ} on output 47, output 66, \mathrm{CZ} on output 47, output 69, \mathrm{CZ} on output 47, output 70, \mathrm{CZ} on output 47, output 73, \mathrm{CZ} on output 47, output 74, \mathrm{CZ} on output 47, output 75, \mathrm{CZ} on output 47, output 77, \mathrm{CZ} on output 47, output 78, \mathrm{CZ} on output 47, output 79, \mathrm{CZ} on output 47, check 80, \mathrm{CZ} on output 47, check 81, \mathrm{CZ} on output 47, check 82, \mathrm{CZ} on output 47, check 89, \mathrm{CZ} on output 47, check 93, \mathrm{CZ} on output 47, check 94, \mathrm{CZ} on output 47, check 95, \mathrm{CZ} on output 47, check 96, \mathrm{CZ} on output 47, check 100, \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 89, \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 96, \mathrm{CZ} on output 51, check 100, \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 89, \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 96, \mathrm{CZ} on output 52, check 100, \mathrm{CZ} on output 53, output 55, \mathrm{CZ} on output 53, output 56, \mathrm{CZ} on output 53, output 60, \mathrm{CZ} on output 53, output 61, \mathrm{CZ} on output 53, output 62, \mathrm{CZ} on output 53, output 64, \mathrm{CZ} on output 53, output 66, \mathrm{CZ} on output 53, output 69, \mathrm{CZ} on output 53, output 70, \mathrm{CZ} on output 53, output 73, \mathrm{CZ} on output 53, output 74, \mathrm{CZ} on output 53, output 75, \mathrm{CZ} on output 53, output 77, \mathrm{CZ} on output 53, output 78, \mathrm{CZ} on output 53, output 79, \mathrm{CZ} on output 53, check 80, \mathrm{CZ} on output 53, check 81, \mathrm{CZ} on output 53, check 82, \mathrm{CZ} on output 53, check 89, \mathrm{CZ} on output 53, check 93, \mathrm{CZ} on output 53, check 94, \mathrm{CZ} on output 53, check 95, \mathrm{CZ} on output 53, check 96, \mathrm{CZ} on output 53, check 100, \mathrm{CZ} on output 55, output 56, \mathrm{CZ} on output 55, output 60, \mathrm{CZ} on output 55, output 61, \mathrm{CZ} on output 55, output 62, \mathrm{CZ} on output 55, output 64, \mathrm{CZ} on output 55, output 66, \mathrm{CZ} on output 55, output 69, \mathrm{CZ} on output 55, output 70, \mathrm{CZ} on output 55, output 73, \mathrm{CZ} on output 55, output 74, \mathrm{CZ} on output 55, output 75, \mathrm{CZ} on output 55, output 77, \mathrm{CZ} on output 55, output 78, \mathrm{CZ} on output 55, output 79, \mathrm{CZ} on output 55, check 80, \mathrm{CZ} on output 55, check 81, \mathrm{CZ} on output 55, check 82, \mathrm{CZ} on output 55, check 89, \mathrm{CZ} on output 55, check 93, \mathrm{CZ} on output 55, check 94, \mathrm{CZ} on output 55, check 95, \mathrm{CZ} on output 55, check 96, \mathrm{CZ} on output 55, check 100, \mathrm{CZ} on output 56, output 60, \mathrm{CZ} on output 56, output 61, \mathrm{CZ} on output 56, output 62, \mathrm{CZ} on output 56, output 64, \mathrm{CZ} on output 56, output 66, \mathrm{CZ} on output 56, output 69, \mathrm{CZ} on output 56, output 70, \mathrm{CZ} on output 56, output 73, \mathrm{CZ} on output 56, output 74, \mathrm{CZ} on output 56, output 75, \mathrm{CZ} on output 56, output 77, \mathrm{CZ} on output 56, output 78, \mathrm{CZ} on output 56, output 79, \mathrm{CZ} on output 56, check 80, \mathrm{CZ} on output 56, check 81, \mathrm{CZ} on output 56, check 82, \mathrm{CZ} on output 56, check 89, \mathrm{CZ} on output 56, check 93, \mathrm{CZ} on output 56, check 94, \mathrm{CZ} on output 56, check 95, \mathrm{CZ} on output 56, check 96, \mathrm{CZ} on output 56, check 100, \mathrm{CZ} on output 60, output 61, \mathrm{CZ} on output 60, output 62, \mathrm{CZ} on output 60, output 64, \mathrm{CZ} on output 60, output 66, \mathrm{CZ} on output 60, output 69, \mathrm{CZ} on output 60, output 70, \mathrm{CZ} on output 60, output 73, \mathrm{CZ} on output 60, output 74, \mathrm{CZ} on output 60, output 75, \mathrm{CZ} on output 60, output 77, \mathrm{CZ} on output 60, output 78, \mathrm{CZ} on output 60, output 79, \mathrm{CZ} on output 60, check 80, \mathrm{CZ} on output 60, check 81, \mathrm{CZ} on output 60, check 82, \mathrm{CZ} on output 60, check 89, \mathrm{CZ} on output 60, check 93, \mathrm{CZ} on output 60, check 94, \mathrm{CZ} on output 60, check 95, \mathrm{CZ} on output 60, check 96, \mathrm{CZ} on output 60, check 100, \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 89, \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 96, \mathrm{CZ} on output 61, check 100, \mathrm{CZ} on output 62, output 64, \mathrm{CZ} on output 62, output 66, \mathrm{CZ} on output 62, output 69, \mathrm{CZ} on output 62, output 70, \mathrm{CZ} on output 62, output 73, \mathrm{CZ} on output 62, output 74, \mathrm{CZ} on output 62, output 75, \mathrm{CZ} on output 62, output 77, \mathrm{CZ} on output 62, output 78, \mathrm{CZ} on output 62, output 79, \mathrm{CZ} on output 62, check 80, \mathrm{CZ} on output 62, check 81, \mathrm{CZ} on output 62, check 82, \mathrm{CZ} on output 62, check 89, \mathrm{CZ} on output 62, check 93, \mathrm{CZ} on output 62, check 94, \mathrm{CZ} on output 62, check 95, \mathrm{CZ} on output 62, check 96, \mathrm{CZ} on output 62, check 100, \mathrm{CZ} on output 64, output 66, \mathrm{CZ} on output 64, output 69, \mathrm{CZ} on output 64, output 70, \mathrm{CZ} on output 64, output 73, \mathrm{CZ} on output 64, output 74, \mathrm{CZ} on output 64, output 75, \mathrm{CZ} on output 64, output 77, \mathrm{CZ} on output 64, output 78, \mathrm{CZ} on output 64, output 79, \mathrm{CZ} on output 64, check 80, \mathrm{CZ} on output 64, check 81, \mathrm{CZ} on output 64, check 82, \mathrm{CZ} on output 64, check 89, \mathrm{CZ} on output 64, check 93, \mathrm{CZ} on output 64, check 94, \mathrm{CZ} on output 64, check 95, \mathrm{CZ} on output 64, check 96, \mathrm{CZ} on output 64, check 100, \mathrm{CZ} on output 66, output 69, \mathrm{CZ} on output 66, output 70, \mathrm{CZ} on output 66, output 73, \mathrm{CZ} on output 66, output 74, \mathrm{CZ} on output 66, output 75, \mathrm{CZ} on output 66, output 77, \mathrm{CZ} on output 66, output 78, \mathrm{CZ} on output 66, output 79, \mathrm{CZ} on output 66, check 80, \mathrm{CZ} on output 66, check 81, \mathrm{CZ} on output 66, check 82, \mathrm{CZ} on output 66, check 89, \mathrm{CZ} on output 66, check 93, \mathrm{CZ} on output 66, check 94, \mathrm{CZ} on output 66, check 95, \mathrm{CZ} on output 66, check 96, \mathrm{CZ} on output 66, check 100, \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 89, \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 96, \mathrm{CZ} on output 69, check 100, \mathrm{CZ} on output 70, output 73, \mathrm{CZ} on output 70, output 74, \mathrm{CZ} on output 70, output 75, \mathrm{CZ} on output 70, output 77, \mathrm{CZ} on output 70, output 78, \mathrm{CZ} on output 70, output 79, \mathrm{CZ} on output 70, check 80, \mathrm{CZ} on output 70, check 81, \mathrm{CZ} on output 70, check 82, \mathrm{CZ} on output 70, check 89, \mathrm{CZ} on output 70, check 93, \mathrm{CZ} on output 70, check 94, \mathrm{CZ} on output 70, check 95, \mathrm{CZ} on output 70, check 96, \mathrm{CZ} on output 70, check 100, \mathrm{CZ} on output 73, output 74, \mathrm{CZ} on output 73, output 75, \mathrm{CZ} on output 73, output 77, \mathrm{CZ} on output 73, output 78, \mathrm{CZ} on output 73, output 79, \mathrm{CZ} on output 73, check 80, \mathrm{CZ} on output 73, check 81, \mathrm{CZ} on output 73, check 82, \mathrm{CZ} on output 73, check 89, \mathrm{CZ} on output 73, check 93, \mathrm{CZ} on output 73, check 94, \mathrm{CZ} on output 73, check 95, \mathrm{CZ} on output 73, check 96, \mathrm{CZ} on output 73, check 100, \mathrm{CZ} on output 74, output 75, \mathrm{CZ} on output 74, output 77, \mathrm{CZ} on output 74, output 78, \mathrm{CZ} on output 74, output 79, \mathrm{CZ} on output 74, check 80, \mathrm{CZ} on output 74, check 81, \mathrm{CZ} on output 74, check 82, \mathrm{CZ} on output 74, check 89, \mathrm{CZ} on output 74, check 93, \mathrm{CZ} on output 74, check 94, \mathrm{CZ} on output 74, check 95, \mathrm{CZ} on output 74, check 96, \mathrm{CZ} on output 74, check 100, \mathrm{CZ} on output 75, output 77, \mathrm{CZ} on output 75, output 78, \mathrm{CZ} on output 75, output 79, \mathrm{CZ} on output 75, check 80, \mathrm{CZ} on output 75, check 81, \mathrm{CZ} on output 75, check 82, \mathrm{CZ} on output 75, check 89, \mathrm{CZ} on output 75, check 93, \mathrm{CZ} on output 75, check 94, \mathrm{CZ} on output 75, check 95, \mathrm{CZ} on output 75, check 96, \mathrm{CZ} on output 75, check 100, \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 89, \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 96, \mathrm{CZ} on output 77, check 100, \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 89, \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 96, \mathrm{CZ} on output 78, check 100, \mathrm{CZ} on output 79, check 80, \mathrm{CZ} on output 79, check 81, \mathrm{CZ} on output 79, check 82, \mathrm{CZ} on output 79, check 89, \mathrm{CZ} on output 79, check 93, \mathrm{CZ} on output 79, check 94, \mathrm{CZ} on output 79, check 95, \mathrm{CZ} on output 79, check 96, \mathrm{CZ} on output 79, check 100, \mathrm{CZ} on check 80, check 81, \mathrm{CZ} on check 80, check 82, \mathrm{CZ} on check 80, check 89, \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 96, \mathrm{CZ} on check 80, check 100, \mathrm{CZ} on check 81, check 82, \mathrm{CZ} on check 81, check 89, \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 96, \mathrm{CZ} on check 81, check 100, \mathrm{CZ} on check 82, check 89, \mathrm{CZ} on check 82, check 93, \mathrm{CZ} on check 82, check 94, \mathrm{CZ} on check 82, check 95, \mathrm{CZ} on check 82, check 96, \mathrm{CZ} on check 82, check 100, \mathrm{CZ} on check 89, check 93, \mathrm{CZ} on check 89, check 94, \mathrm{CZ} on check 89, check 95, \mathrm{CZ} on check 89, check 96, \mathrm{CZ} on check 89, check 100, \mathrm{CZ} on check 93, check 94, \mathrm{CZ} on check 93, check 95, \mathrm{CZ} on check 93, check 96, \mathrm{CZ} on check 93, check 100, \mathrm{CZ} on check 94, check 95, \mathrm{CZ} on check 94, check 96, \mathrm{CZ} on check 94, check 100, \mathrm{CZ} on check 95, check 96, \mathrm{CZ} on check 95, check 100, \mathrm{CZ} on check 96, check 100
Or no Clifford gate at all: run \mathrm{T}^3 on rotations 3, 4, 5, 6, 17, 18, 27, 38, 41, 44, 56, 57, 60, 62, 64, 65, 76, 78, 83, 88, 89, 98, 99, 100 and 125 more (listed below); \mathrm{T}^5 on rotations 1, 10, 11, 12, 22, 25, 32, 34, 36, 46, 52, 54, 84, 90, 104, 105, 109, 117, 127, 140, 156, 158, 168, 209 and 1 more (listed below); \mathrm{T}^\dagger on rotations 9, 13, 15, 16, 19, 21, 30, 31, 33, 35, 40, 42, 53, 55, 66, 71, 80, 102, 103, 113, 119, 128, 130, 134 and 2 more (listed below), 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 149 rotations at T³
3, 4, 5, 6, 17, 18, 27, 38, 41, 44, 56, 57, 60, 62, 64, 65, 76, 78, 83, 88, 89, 98, 99, 100, 107, 108, 111, 114, 115, 121, 125, 131, 132, 136, 143, 148, 149, 150, 151, 152, 155, 157, 159, 161, 163, 165, 169, 170, 177, 179, 180, 181, 182, 183, 186, 189, 192, 193, 194, 196, 198, 199, 203, 206, 207, 213, 216, 218, 220, 227, 229, 230, 231, 232, 234, 240, 243, 244, 247, 252, 255, 257, 258, 259, 261, 262, 263, 267, 270, 271, 278, 283, 284, 285, 287, 290, 294, 297, 298, 303, 305, 307, 309, 319, 320, 321, 326, 328, 331, 336, 337, 341, 342, 343, 345, 346, 348, 352, 354, 357, 359, 360, 362, 364, 365, 366, 373, 374, 378, 380, 382, 385, 387, 390, 391, 392, 393, 394, 396, 403, 404, 406, 410, 411, 417, 419, 423, 426, 429
All 25 rotations at T⁵
1, 10, 11, 12, 22, 25, 32, 34, 36, 46, 52, 54, 84, 90, 104, 105, 109, 117, 127, 140, 156, 158, 168, 209, 214
All 26 rotations at T†
9, 13, 15, 16, 19, 21, 30, 31, 33, 35, 40, 42, 53, 55, 66, 71, 80, 102, 103, 113, 119, 128, 130, 134, 265, 315
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/430.80.4.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-430.80.4.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 7,262 faults of weight 4 are undetectable and damaging, so A_{4}=7{,}262. 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_430_80_4_284672c3c5ec.json",
"label": "paired_column_contraction_430_80_4_284672c3c5ec",
"N": 101,
"d": 4,
"d_is_exact": true,
"origin": "Existing triorthogonal code with physical paired-column contraction",
"provenance": "gamma frontier release record paired_column_contraction_430_80_4_284672c3c5ec (source catalogue id paired_column_contraction_430_80_4_284672c3c5ec); construction: Existing triorthogonal code with physical paired-column contraction; matrix 284672c3c5ecf884...; the release states d=4 (exact), gamma=1.213132377351049 (exact)",
"notes": "matrix gamma_frontier_release/matrices/284672c3c5ecf884c68617d808b826a9b3b7ff150a89cf86a97837561439cf0f.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/430.80.4.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[1051].