An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University (nebe@math.rwth-aachen.de) and
Neil J. A. Sloane (njasloane@gmail.com)

Last modified Sat Oct 17 06:02:11 PM CEST 2026

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
SUBGROUP_ORDER
SUBGROUP_NAME
SUBGROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  X4969
  

• DIMENSION
  88
  

• DET
  1
  

• GRAM
  88 0
  30
  -12 34
  -6 15 32
  -7 4 -8 30
  13 6 -7 -8 38
  3 -2 8 -3 -13 34
  13 -7 -13 -2 6 -13 38
  -10 -4 -6 8 -17 15 0 40
  2 8 1 10 10 2 -8 -8 32
  7 -15 -13 -9 -5 -5 19 -4 -18 42
  -13 6 11 -4 -3 6 -13 4 -4 1 30
  -1 -10 4 1 -15 7 -11 1 -2 -6 -5 30
  -4 16 15 -3 3 -3 0 -6 11 -16 -4 -7 34
  -2 15 12 0 1 -5 9 -7 -5 -5 -4 -8 10 34
  15 6 2 -3 11 13 -6 0 5 -9 -2 -7 -1 -3 36
  9 -17 5 -14 -8 -5 13 4 -17 10 -5 11 -6 -4 0 46
  9 3 -11 10 2 5 3 10 6 0 -13 -4 -8 -1 12 -3 34
  3 3 -4 8 6 9 -12 5 6 -12 0 -5 1 -7 17 -16 5 30
  5 -11 3 -15 -7 3 -2 -5 -8 15 3 12 -10 -9 -6 10 -10 -5 34
  14 -17 -13 6 5 -2 -3 2 -5 -5 -13 12 -13 -12 3 6 6 8 5 44
  -3 -13 -10 -2 -4 -3 6 5 0 8 4 2 -11 -12 -5 7 -7 -4 5 1 30
  -1 -5 -10 4 -10 0 4 -2 -9 10 2 5 -16 2 -5 -5 4 -6 7 7 2 38
  -12 7 -4 10 -11 8 -13 12 -6 -8 2 10 -9 -4 6 -4 3 4 -4 9 3 11 38
  -1 14 9 4 5 -6 -1 -3 3 -1 7 -13 7 5 1 -11 0 5 -5 -2 -6 -5 -10 32
  3 2 12 0 -2 9 -10 -5 4 -5 4 10 -2 -6 1 -2 2 -1 3 5 -3 1 -2 2 28
  -7 16 14 -10 -1 4 -13 -8 -4 3 14 3 1 6 -5 -7 -4 -6 7 -8 -5 6 4 8 8 40
  7 -14 -8 -6 0 1 11 3 1 8 -12 -4 6 -1 -6 2 0 -6 -3 -2 0 -8 -13 -5 -7 -10 34
  2 -4 0 10 -8 -8 12 -3 4 11 3 0 -3 -1 -8 2 -2 -9 0 -4 14 2 -5 6 7 -5 -3 38
  -5 14 -2 -7 9 -1 3 -1 6 5 10 -19 8 -2 3 -12 1 5 1 -19 -1 -4 -9 11 -8 8 1 -8 38
  -1 12 15 -7 10 0 1 2 4 -16 -1 -5 15 14 8 8 2 -5 -13 -8 -5 -13 -2 -2 0 1 1 -4 -7 38
  -11 7 11 -6 -8 5 -13 0 4 -10 2 2 17 4 -6 -3 -5 -1 1 -11 -4 -9 2 -7 -3 8 1 -10 4 7 30
  1 6 -7 -7 13 -10 5 -5 -2 3 -4 0 -1 0 -3 -4 1 -6 4 3 -3 3 1 4 -4 6 -2 -3 5 0 -2 26
  3 12 15 -12 10 -4 10 1 1 0 1 -5 7 8 6 19 1 -11 5 -13 -4 -14 -10 7 2 5 -7 1 6 21 -1 7 46
  -11 15 -1 -3 4 -2 -4 -8 -6 1 2 3 -6 3 -1 -6 -2 2 -2 -6 3 5 16 -2 1 13 -17 -10 8 -5 2 10 -1 44
  -5 11 12 -9 -5 7 2 10 -12 -8 3 1 5 9 9 12 0 0 1 -3 1 -2 8 1 -2 1 -13 -6 2 13 6 4 14 13 38
  -10 16 -4 1 9 -8 0 -2 8 0 10 -10 9 1 0 -14 -1 -3 -5 -21 -5 -1 -1 0 -8 9 -2 0 19 3 4 9 6 0 -4 40
  -7 16 3 7 -1 10 -9 6 3 -8 10 0 -2 -4 10 -12 1 7 -6 -6 -5 2 16 7 5 5 -11 -6 9 -4 -4 3 1 14 5 9 30
  5 -2 2 -6 0 13 -4 6 -2 -3 7 -1 -8 3 9 -1 -1 6 2 1 2 5 3 0 -1 7 1 -5 3 2 -5 -3 -2 -1 -1 -5 3 24
  4 5 -9 -5 3 3 2 3 -3 1 -9 5 1 -4 4 -7 4 7 3 1 -1 -2 8 -1 -5 6 6 -11 7 -6 0 12 -4 14 3 6 11 2 34
  -12 17 19 4 -14 -6 -2 -11 -7 5 10 -6 11 16 -11 -1 -12 -7 -3 -16 -8 0 -2 14 5 16 -8 6 6 -2 7 -9 0 10 2 1 5 -3 -9 48
  -3 -13 4 -11 -11 -2 9 -4 -16 9 -5 16 3 0 -12 20 -18 -11 10 -4 2 3 1 -19 0 -5 9 0 -14 2 3 0 0 3 6 -5 -9 -7 3 2 44
  7 -8 1 -13 -7 8 2 1 -14 10 -3 10 -10 3 -2 11 -3 -7 18 7 -3 9 4 -8 -1 9 2 -6 -4 -8 1 7 1 3 4 -10 -4 9 5 -2 9 28
  1 -4 0 -1 3 6 -13 4 7 -11 2 8 -6 -15 2 3 3 2 0 10 2 -7 3 -2 8 -1 2 -9 -2 -2 -2 -1 -4 4 -2 -7 6 2 5 -6 -4 -1 28
  -10 -5 -8 -5 1 -17 4 -7 -4 4 -4 0 -2 2 -15 2 -6 -11 6 -4 4 7 -3 -6 -13 -6 7 -6 6 -8 6 11 -6 5 0 3 -10 -9 0 -5 11 4 0 36
  12 7 14 -15 4 3 -4 -17 -7 4 3 7 -1 11 12 12 -3 -4 14 1 -5 -1 2 1 0 19 -14 -1 -1 4 2 3 13 6 13 -1 -1 6 3 6 -1 14 -6 -8 46
  -2 -11 -15 7 -13 14 -10 8 8 5 -9 10 -7 -13 0 -11 14 1 3 2 0 13 9 -13 -1 -5 9 -7 -4 -10 5 1 -13 -5 -10 3 1 -3 8 -17 -1 2 3 3 -11 48
  -3 -4 -7 10 -2 -11 6 6 0 7 4 -11 -5 -8 -4 4 4 -4 -7 -2 4 -4 -3 6 -5 -11 4 10 2 -5 -2 -3 -1 -9 -10 3 1 -8 -8 3 -8 -9 3 6 -17 -5 32
  5 0 6 -13 11 10 2 1 6 -2 1 2 0 4 6 0 -5 1 8 -13 0 -12 -8 -8 0 -2 8 -6 3 14 0 3 16 -1 1 3 2 10 5 -14 6 6 0 -3 4 -3 -12 40
  2 -5 -3 2 1 -12 14 0 2 1 -4 0 3 -2 -12 5 -1 -10 -2 -2 3 -1 -11 0 4 -8 11 14 -1 0 -3 4 2 -10 -8 2 -7 -4 -1 -3 7 -2 0 8 -14 -7 13 0 28
  -7 6 -5 12 6 3 -3 7 10 -3 0 -4 -7 -7 6 -7 12 2 -13 -2 4 -4 8 -2 5 -1 -2 -1 -1 6 -7 -3 5 6 -2 3 8 -6 -4 -7 -7 -12 8 -4 -13 7 6 2 -4 34
  2 4 -5 9 0 9 0 6 -1 -6 -6 1 -8 3 15 -2 9 13 -9 5 2 -2 17 -9 -4 -6 -4 -3 -4 4 -5 -6 -7 12 9 -5 8 7 6 -3 -1 0 2 -9 5 -3 -4 5 -8 10 32
  15 -1 -1 -14 2 7 6 -4 1 4 -9 1 -2 4 7 9 6 -5 9 -2 3 -4 -1 -6 -3 4 2 -5 4 -2 8 4 8 6 4 -6 -1 8 12 -1 -6 15 3 -2 17 -1 -4 7 -2 -12 2 40
  13 -9 8 -1 5 -7 -4 -11 -2 -10 -5 9 -2 7 5 11 -3 3 2 11 -10 1 -11 0 5 -1 3 -2 -19 7 -5 -3 1 -15 -8 -10 -11 7 -5 -3 6 4 0 -2 6 -7 -3 4 7 -11 -5 -4 44
  -1 -9 -1 2 -6 13 0 12 -6 8 3 -3 -11 3 5 2 8 0 -9 -7 0 1 2 -8 2 -4 10 3 -11 7 -6 -12 0 -9 -5 -4 -3 6 -8 -9 5 -1 -4 -8 -8 9 3 8 -2 13 7 -8 4 36
  -11 6 6 11 -16 2 -4 8 -3 1 8 5 -4 -2 0 2 3 -1 0 -8 3 3 10 3 1 2 -10 11 -2 -1 1 -4 3 0 8 3 8 -6 -1 4 1 -4 -5 -1 2 4 9 -6 2 7 5 -9 -4 5 28
  15 5 -1 -10 8 10 3 -11 -2 14 -2 -1 -2 -5 18 -6 3 5 12 -4 -5 1 2 -2 5 9 0 -3 8 -7 -4 6 4 7 4 8 10 -1 16 -4 3 7 -4 -9 19 6 -10 9 -8 2 7 9 -5 -1 1 42
  -14 -6 -13 17 -7 -4 -6 13 11 -5 1 9 -12 -16 -9 -1 2 -2 -5 3 18 -2 16 -10 -3 -8 1 9 -6 -4 -3 -4 -8 2 -11 4 4 -1 -1 -10 -4 -9 10 3 -18 11 11 0 6 17 8 -8 -7 4 9 -14 42
  15 -2 -7 5 1 4 13 -2 -5 11 -4 -5 -5 0 7 -3 8 7 0 5 -3 3 -5 3 3 -1 0 6 2 -11 -10 -4 -7 -1 -1 0 3 0 9 2 -4 0 -4 -12 5 -4 4 -8 2 -2 8 5 0 1 3 16 -10 30
  -2 -12 4 -8 -7 4 -3 1 2 4 7 -1 -2 -6 -4 6 -11 -8 5 -8 11 -2 -5 -3 0 -5 14 7 -3 2 2 -6 -1 -12 -7 -3 -6 6 -6 0 8 1 7 5 -10 5 8 5 7 -3 -8 2 3 9 -1 -7 7 -9 30
  -14 10 1 14 -4 -2 -1 2 -2 0 2 -8 -2 12 -5 -12 3 6 -13 -5 1 1 7 6 -1 3 -6 3 2 2 -1 -6 -4 12 3 -4 2 0 -6 14 -4 -9 -7 0 -7 -3 0 -6 -6 13 13 -13 -8 9 8 -8 5 0 -6 32
  -14 -3 1 10 -23 4 -2 8 -1 11 10 6 -8 -2 -11 -4 -2 -6 6 -14 6 17 1 -1 2 3 -4 15 -1 -8 -3 -7 -5 -4 -6 6 0 1 -10 8 5 -1 -10 1 -10 14 3 -1 2 2 -6 -15 -3 10 15 -6 11 -4 7 6 38
  -9 3 -1 4 3 0 -10 11 0 -3 6 -2 -10 1 -6 -8 5 -1 -4 -1 0 -5 6 3 -1 4 -3 -2 -8 6 -1 3 1 2 -7 0 0 3 -2 -5 -12 -1 7 0 -8 1 7 5 -2 8 -1 -1 0 10 -1 -12 12 -8 4 3 1 34
  -2 3 3 -7 -1 2 9 12 0 -3 1 -9 8 9 1 8 4 -8 -4 -9 2 -1 -2 1 -10 -4 2 0 7 12 6 3 14 -6 14 3 -5 3 -6 -6 -3 1 -6 4 -1 -2 0 3 1 -4 -6 6 -7 3 -2 -10 -4 -9 4 -3 0 0 28
  8 10 -8 -7 12 -8 12 -15 4 13 -13 -14 8 5 5 -8 9 0 1 -11 -10 -3 -8 5 -10 -3 5 -4 16 -4 4 14 6 9 -3 10 3 -7 14 1 -5 2 -8 8 5 5 4 2 1 -5 -2 17 -12 -9 -5 15 -14 7 -6 -3 -9 -6 1 44
  8 2 0 -2 13 -12 -2 -16 4 -5 -7 -6 6 6 7 -4 0 3 -1 7 -5 0 -3 1 -3 -1 0 0 -6 7 3 4 -3 -7 -5 2 -10 -3 -3 -1 -4 -1 -5 4 6 -3 0 -3 0 -6 -2 1 14 -6 -6 2 -7 -2 1 -4 -9 1 -3 6 24
  -10 2 -4 12 -12 9 -3 13 -2 -2 4 -4 -7 5 4 -12 0 12 -5 -3 10 3 14 -2 -8 -9 -5 7 -1 -3 -3 -9 -14 6 7 -4 5 7 0 2 -4 -4 -4 -3 -5 1 -1 0 -10 4 19 -5 -12 9 8 -5 9 3 2 17 10 5 1 -6 -5 34
  7 -7 -13 -10 11 -15 4 -6 -15 14 -9 -3 -9 -3 1 11 6 -1 3 13 -4 -2 -2 2 -8 -3 4 -9 0 -6 -5 13 0 8 0 -3 -6 -4 9 -4 0 6 3 11 7 -2 4 -7 -2 -8 -2 8 3 -5 -10 2 -7 0 -5 -5 -15 3 -3 16 7 -9 38
  2 -11 -4 8 -11 8 -6 -1 -4 -2 -4 9 -2 4 3 -6 -7 11 -1 11 4 3 5 -9 -3 -8 -2 1 -13 -7 3 -11 -23 -2 0 -8 -5 3 -3 2 4 0 -7 -5 5 5 -9 -4 -11 -7 12 -3 2 1 -2 -1 -2 6 -5 7 3 -8 -9 -9 2 17 -3 42
  -8 -3 -7 14 3 -3 0 -1 -1 0 11 0 -16 0 -7 -12 -7 6 -8 -1 7 11 4 -2 5 -1 -6 7 -6 -8 -15 -5 -14 8 -10 -1 7 5 -6 3 3 -5 1 -1 -13 -4 1 3 3 12 9 -18 7 11 4 -6 14 3 0 15 11 7 -14 -16 -4 11 -10 3 42
  -10 2 -6 -4 -4 -12 -2 -1 -16 6 -3 8 -5 3 -8 5 -6 -9 7 3 -3 5 15 -5 -10 3 0 -8 -2 -7 3 15 -3 10 6 9 6 -6 12 3 11 10 -3 16 8 3 -2 -4 -2 -8 0 2 -2 -8 2 4 3 -7 -4 -3 -4 1 -3 8 2 -2 19 0 -4 38
  -11 6 -4 -1 -9 -10 15 1 -6 18 -1 -13 6 6 -12 1 1 -12 1 -20 0 9 -1 -2 -10 -1 6 3 15 -3 4 0 1 5 -2 11 -3 -7 -2 15 7 -1 -11 13 -12 3 8 -6 5 0 -6 -3 -16 0 2 -2 0 -2 3 7 13 -4 9 15 -3 3 0 -10 -5 5 38
  -8 3 7 4 -12 3 -14 -8 6 3 5 13 3 -9 -12 -11 -4 -5 7 -5 -5 8 3 1 12 17 0 5 -5 -7 6 1 -9 1 -13 6 2 -7 3 9 9 -2 3 0 -5 13 0 -7 3 3 -11 -9 1 -1 8 5 4 -1 5 -2 15 2 -12 -3 -2 -8 -9 -3 0 -1 3 38
  -2 6 -9 -6 8 -4 -3 0 4 2 -6 -7 -2 1 6 -7 14 3 -2 -3 7 -2 1 1 -6 6 2 -7 11 1 5 5 0 8 3 8 -1 0 11 -9 -15 -4 -1 5 5 7 -5 2 -8 5 2 10 -9 -1 -5 4 4 -4 -5 2 -6 3 5 13 4 2 13 -3 -9 8 3 -9 36
  -7 -7 -2 7 -19 2 -11 4 -3 -6 -8 13 -5 -5 -4 -1 0 3 7 10 0 14 12 -7 3 -9 2 -3 -13 -12 2 -7 -18 -3 -3 -11 0 -2 0 1 8 4 4 9 -10 13 0 -11 0 -5 1 -3 7 0 2 -6 7 -5 6 -2 8 0 -7 -5 2 7 1 7 1 11 3 8 0 36
  0 3 -3 10 7 -11 0 -4 1 -3 -8 0 0 2 -4 -6 4 1 -8 8 -4 -10 -3 9 2 -4 2 2 -5 -2 -5 6 -3 4 -2 -4 -1 -11 3 2 -6 -5 5 4 -4 -2 5 -6 3 7 1 -8 4 -5 1 0 3 3 -7 6 -7 8 -10 0 5 -2 8 -1 5 5 -7 -1 0 -2 28
  12 3 5 -6 -3 12 13 8 -7 2 -10 3 9 8 3 8 4 -4 1 0 -14 -3 -4 -3 2 5 5 -6 -4 9 3 5 12 -2 9 -1 0 3 7 2 8 12 -5 -13 5 -2 -7 6 1 -7 2 11 2 0 -7 12 -16 11 -8 -8 -5 -3 5 5 -4 -9 -3 -1 -13 -4 -1 0 -12 -7 -1 42
  6 -15 -14 -1 0 9 -8 0 -1 14 -2 7 -17 -10 -4 -10 6 6 13 11 -2 5 -3 -3 0 2 8 -9 2 -21 -6 0 -15 -3 -15 -2 -2 4 8 -11 -4 9 7 3 2 19 -7 5 -9 -1 -1 4 -3 5 -8 8 1 4 -1 -2 2 5 -11 4 -5 0 11 9 3 5 -7 4 9 5 1 -6 40
  -8 8 10 -4 7 -4 -9 1 0 -15 9 4 9 -2 -2 2 -8 5 -6 -1 -4 -7 -2 3 5 8 -7 -6 0 14 3 1 6 6 5 4 2 2 -1 2 4 -6 6 -5 -1 -15 -5 5 3 0 -1 -11 8 -4 -2 -9 0 -9 -5 -1 -3 3 -3 -11 -1 -7 -1 -4 5 -3 -8 3 -5 -5 0 2 -10 30
  5 7 -9 -1 6 4 7 -1 2 -2 -14 2 -1 2 10 -1 11 1 -4 2 -4 6 11 -6 -5 -3 -4 -11 5 0 -5 9 3 18 9 3 8 1 12 -8 -1 5 -1 0 5 8 -11 2 -7 3 11 11 -12 -5 -6 10 -1 3 -12 -2 -6 -3 4 14 -3 0 5 -2 -7 6 3 -6 6 0 0 12 1 -4 32
  -7 4 -5 -1 10 4 -4 3 1 3 16 -14 -1 1 -2 -21 -4 7 -2 -7 2 3 -2 2 -1 9 -4 -2 15 -3 2 2 -5 1 -3 16 2 5 -3 -4 -11 -4 -7 -2 -5 3 -4 3 -6 3 -4 -10 -10 5 -4 3 -2 2 -1 8 4 5 3 -4 0 6 -7 2 11 -5 2 -3 5 -13 -2 -5 7 0 -5 34
  11 -6 1 6 4 -11 16 -3 8 -7 -18 6 2 12 -2 18 9 -10 -9 1 4 -7 -13 -4 2 -9 7 10 -16 17 -6 -5 18 -13 -2 -7 -15 -2 -6 -5 4 -6 -4 -3 1 -3 -2 7 12 4 0 5 22 6 -1 -10 7 -2 1 1 -1 -1 4 -8 5 -10 -4 -4 2 -8 -8 -9 2 -4 7 6 -9 0 0 -14 50
  -15 -1 3 0 1 -12 -15 -4 -2 -10 7 4 1 1 -12 1 -14 1 -2 0 4 -9 4 -3 -7 1 -4 -8 -6 2 12 -3 -8 6 -5 0 -3 -3 -3 5 2 -5 5 11 -2 -8 5 -2 -3 -5 -3 -3 7 -4 -1 -19 11 -14 4 3 -5 13 -5 -7 5 2 7 5 6 11 -4 -1 4 6 3 -17 0 10 -11 0 -2 34
  -14 5 -10 19 1 -19 -4 8 8 -14 -10 -2 4 0 -13 -13 9 0 -17 9 1 1 3 8 -3 -4 2 1 -8 3 1 5 -8 -4 -12 2 -6 -11 -2 -3 -12 -14 3 11 -25 6 13 -16 10 11 -7 -14 3 -4 2 -24 17 -11 -3 8 3 17 -2 -5 8 -1 3 -4 4 2 2 6 7 11 16 -9 -6 6 -4 -3 11 13 50
  -5 5 1 0 9 -13 -6 -11 12 -13 2 5 7 1 -12 -7 -8 -7 -1 -2 3 0 -5 2 -1 10 -4 -1 -1 2 6 9 0 1 -7 10 -4 -4 2 -1 -3 -5 6 10 2 0 -3 -4 5 -3 -13 1 7 -15 -5 -8 5 -9 1 -7 -4 7 -2 -4 7 -11 -3 -6 3 3 -7 8 2 -1 6 -5 -3 8 -3 2 9 13 17 32
  -6 5 14 1 -10 10 1 4 -8 -7 -2 5 7 12 1 1 -4 0 -4 0 -8 2 1 1 9 -1 1 -2 -8 8 -1 -7 2 -1 16 -7 2 -2 -4 5 14 0 -8 -4 -1 -5 -10 2 -1 4 6 -13 1 11 8 0 -10 4 -4 11 5 -10 1 -9 -6 6 -11 8 3 -2 -2 1 -7 5 -1 7 -6 2 2 -2 2 -8 -5 -13 38
  9 -6 5 -6 -7 2 12 -7 -8 8 -8 8 -5 13 -6 8 0 -11 13 5 -4 13 -7 -2 6 -3 3 7 -9 -3 -7 2 3 -4 8 -13 -7 1 -2 1 12 13 -6 6 10 -2 -10 4 4 -10 -2 6 6 1 -1 3 -14 5 0 -1 3 -10 3 3 -1 0 2 3 -2 3 1 -1 -4 7 -4 5 5 -10 1 -9 7 -12 -14 -7 16 34
  -13 0 -4 -6 -8 -8 9 9 -19 14 12 -10 2 -2 -14 7 -9 -7 -1 -10 7 4 5 0 -7 5 0 0 14 -9 6 1 -5 9 6 6 1 -3 3 13 9 0 -5 10 -9 -9 10 -15 6 -7 -8 -2 -15 -3 3 -6 -1 2 3 4 2 -3 8 0 -8 1 6 -7 0 10 21 -1 -1 -3 -6 -3 -9 0 -5 10 -15 6 -1 -3 -3 -6 42
  3 -15 -13 2 -12 -1 12 6 -10 9 -11 12 -14 4 -12 12 7 -11 6 8 3 19 5 -13 -6 -8 5 -2 -10 -8 -4 1 -4 1 0 -8 -4 1 5 -8 10 10 -2 9 -1 14 -2 -3 3 -8 0 9 3 4 0 -7 4 2 0 -3 5 -2 4 0 -7 0 7 2 1 11 4 -3 1 12 -5 3 9 -10 8 -9 11 -1 -1 -1 0 16 2 34
  

• DIVISORS
  1
  

• MINIMAL_NORM
  8
  

• KISSING_NUMBER
  168498000
  

• HERMITE_NUMBER
  8
  

• SUBGROUP_ORDER
  2^2*5*23
  

• SUBGROUP_NAME
  C115 : C4
  

• SUBGROUP_GENERATORS
  2
  88 88
  -144 -168 -42 -29 128 39 68 38 -37 -61 -33 48 20 -16 86 -37 16 -57 81 -58 -102 -6 6 23 -42 61 -31 87 2 40 9 -31 -8 11 -28 -50 27 -35 17 51 -40 -21 3 19 -11 -1 -15 -27 6 2 19 1 18 -13 1 -3 8 5 13 -2 -3 -16 -1 -2 -3 4 -2 6 -4 -5 -8 -3 5 8 -6 1 5 -5 4 1 2 -2 -7 -2 3 -1 4 -1
  185 219 81 7 -51 -35 -107 16 2 57 -3 -26 -63 -1 -106 44 -42 36 -95 51 91 33 -24 -28 1 -76 28 -42 15 -48 23 22 7 -15 7 37 -24 21 -13 -34 35 9 -10 -16 -4 15 -3 18 -11 7 -7 -5 -12 8 3 1 -4 6 -5 3 5 8 0 2 -1 -5 -3 -1 0 1 3 2 -1 -5 1 -3 -4 4 1 -4 -3 1 4 1 0 0 -2 -1
  5 -10 46 24 9 18 10 11 -9 15 24 30 25 10 -20 7 3 41 -15 9 29 11 6 -10 19 -13 6 -23 6 6 -26 25 6 5 -13 13 -27 -14 4 10 -26 0 -5 18 11 4 13 -4 -9 -1 10 8 0 11 -14 10 8 2 8 -7 4 -7 9 14 3 -4 -6 -3 5 7 2 1 -1 0 0 -1 -4 2 -3 -5 -2 5 2 1 1 5 0 -4
  14 14 -78 26 -59 -8 -35 -38 34 -13 16 -47 16 33 -6 39 -2 -11 14 -10 23 -3 12 33 40 -12 8 -30 1 -2 4 4 -7 -3 19 5 -13 17 2 -32 30 14 7 -29 8 -15 12 13 5 4 -12 -4 -7 2 4 4 -10 -6 -15 3 1 12 -8 -4 2 1 10 0 5 3 7 4 -4 -5 1 6 3 -1 0 5 -3 0 3 -2 -1 0 -2 2
  -43 -76 -41 11 110 35 -16 38 -41 -44 -31 20 26 -4 31 3 -1 -54 64 -46 -57 10 -4 16 -28 34 -3 65 4 13 2 -19 -7 11 -6 -33 15 -18 10 27 -14 -20 -8 8 -10 3 -3 -15 2 6 15 5 10 -12 4 -5 0 3 8 5 3 -5 -7 -1 -4 -1 -3 6 0 -5 -3 -5 9 4 -10 -2 0 -1 5 0 -3 -2 -4 -2 3 -5 1 -1
  -3 0 228 -10 86 20 59 45 -63 56 -5 95 -24 -56 -27 -64 20 68 -73 37 24 15 -16 -92 -62 -10 4 7 0 -9 -32 21 33 -4 -30 10 -8 -26 7 54 -72 -13 -11 49 -13 18 -14 -26 -10 -13 14 6 2 5 -14 6 21 4 21 -17 3 -26 21 19 3 -2 -14 -2 0 3 -9 -1 3 8 -6 -5 -6 -1 -4 -6 1 7 -1 6 0 4 -2 -4
  -71 -54 -14 -6 58 7 5 3 -17 -5 -36 -10 19 -22 57 -38 38 -63 43 -5 -44 -16 -22 -16 -52 48 -13 49 -22 -8 0 -36 1 3 13 -24 50 11 1 13 10 -12 -6 5 -17 2 -12 -3 13 -11 -5 0 4 -20 9 -14 -4 -3 5 4 -9 0 -8 -14 -7 3 1 4 -1 -11 -7 -5 0 6 0 -1 1 3 2 2 3 0 -7 -3 -1 -6 3 3
  -105 -141 104 10 88 34 79 22 -32 21 -5 67 51 -22 49 -63 46 22 14 2 -29 -11 -1 -57 -36 50 -3 21 -15 14 -54 4 18 9 -3 -10 20 -22 7 49 -58 -17 -7 43 -2 2 2 -27 5 -19 7 14 5 -6 -11 2 16 -4 15 -7 2 -13 8 12 1 0 -9 -2 5 -1 -6 -4 2 9 -5 -5 -4 1 -4 -1 -1 6 -2 2 -2 1 -1 0
  138 191 147 -15 22 -12 -90 50 -8 71 -38 9 -84 -9 -96 21 -45 38 -111 56 80 48 -38 -60 -36 -77 14 -3 28 -48 27 16 14 -24 -5 18 -16 11 5 -3 8 -5 -9 -4 -9 17 -9 1 -14 5 1 -8 -2 5 10 2 0 4 0 -9 2 0 2 2 0 -10 -2 0 1 5 6 8 0 -4 -4 2 0 2 3 -2 -3 1 2 2 2 -1 -1 -4
  -128 -126 -275 36 -22 32 17 -75 8 -89 21 -63 108 34 97 35 46 -82 156 -69 -67 -39 19 108 43 68 -10 13 -40 39 3 -37 -31 27 9 -20 40 8 -15 -27 39 16 15 -20 10 -23 8 14 25 1 -10 5 2 -11 1 -7 -11 -3 -7 21 -2 16 -10 -21 -4 11 9 5 -6 -9 -4 -7 -4 -1 9 -1 2 1 -3 3 5 -6 -4 -6 -1 0 6 5
  84 66 -10 44 -54 -4 -36 -24 -5 3 38 -11 26 7 -50 38 -1 32 -16 7 55 7 6 16 41 -28 25 -59 -7 -8 -17 24 1 8 5 35 -31 4 -11 -24 10 16 -9 -4 15 1 15 14 -3 5 -4 7 -11 11 -14 7 1 0 0 9 9 7 5 8 1 2 -3 -3 3 3 1 -4 -3 -2 2 -4 -7 2 -7 -4 -5 2 4 -2 -1 4 -1 0
  -31 -52 -45 -7 -32 0 36 -10 32 -26 23 3 0 30 10 19 -18 16 11 -20 -9 -3 30 36 47 -6 -7 -17 17 23 6 11 -10 -2 -7 -3 -27 -12 9 -4 -10 6 11 -10 13 -11 10 -3 -5 7 4 -3 3 10 -3 10 1 -2 -7 -5 2 0 1 8 6 3 7 -2 3 8 7 7 -2 -5 0 5 5 -3 1 2 -1 -3 4 2 0 3 -2 -1
  53 82 120 -39 -19 -13 -23 41 34 80 -8 27 -38 25 -53 -4 -20 69 -96 64 62 23 -13 -52 -6 -50 -1 -24 23 -19 -7 29 15 -16 -11 19 -14 -4 -1 4 -10 -7 0 14 9 9 4 -5 -10 -3 3 3 5 6 3 10 8 2 4 -15 1 -1 3 7 2 -11 -5 -5 8 6 9 8 -5 -2 2 4 0 3 0 -1 -2 4 -1 2 3 3 2 -6
  62 76 101 8 -9 -12 -24 10 -11 44 5 2 -17 -19 -41 -13 5 22 -54 42 43 10 -20 -47 -18 -24 8 -19 -3 -28 -12 12 14 -6 3 19 -9 9 2 -2 0 -1 -14 10 -5 12 0 6 -8 -5 0 2 -6 2 -4 -2 2 0 6 -3 -2 -4 4 3 -3 -4 -5 -2 3 1 -2 -1 0 2 1 -2 -5 4 0 -5 0 4 0 0 -2 -1 -1 -2
  28 46 87 -29 42 -9 5 33 -31 15 -27 36 -55 -35 -20 -27 -14 9 -42 8 0 13 -12 -36 -48 -13 -5 26 13 -9 18 -1 11 -8 -15 -7 2 -6 -1 21 -19 -10 0 6 -16 11 -19 -9 -5 0 4 -8 3 1 3 -3 4 6 7 -8 -3 -12 3 2 1 -2 -5 1 -6 -2 -5 0 3 3 -3 0 3 -5 1 -2 1 1 -2 2 3 1 0 -2
  -143 -160 -133 -8 -47 -13 79 -58 39 -51 2 -40 41 4 103 -39 35 -56 85 -35 -77 -50 22 33 15 70 -28 18 -20 29 -6 -31 -16 8 28 -27 39 19 0 -3 15 5 15 -14 3 -19 3 8 16 -8 -15 -7 1 -7 7 -10 -11 -9 -11 3 -15 9 -9 -15 0 5 11 -3 -6 -6 -1 -1 -2 0 6 5 8 -2 -2 6 7 -2 -2 -1 -2 -3 1 5
  19 24 77 -31 105 -7 -11 52 -53 -5 -61 22 -63 -61 11 -36 -15 -48 -7 -10 -50 13 -32 -35 -82 17 -5 76 2 -15 35 -33 3 -7 -5 -25 36 -5 5 30 -6 -16 -10 8 -31 18 -33 -14 2 1 5 -8 2 -16 8 -14 3 8 6 7 -2 -8 -1 -7 -7 4 -5 6 -11 -10 -13 -5 8 7 -8 -7 0 -1 6 0 2 -1 -3 0 0 -7 0 4
  82 105 122 -54 15 -19 -18 49 -13 32 -15 42 -86 -23 -57 -11 -34 39 -90 31 29 29 -13 -34 -36 -50 -1 5 25 -14 25 14 16 -16 -30 6 -24 -19 4 16 -18 -6 -4 6 -10 13 -19 -8 -12 7 10 -7 3 4 1 6 11 10 7 -9 3 -13 7 8 0 -4 -6 1 -1 3 0 2 0 1 -3 2 1 -5 2 -1 -2 1 -1 3 3 3 1 -3
  129 170 60 -58 -13 -30 -42 48 -8 9 -10 14 -111 -23 -76 24 -63 22 -82 23 27 35 -13 9 -11 -68 -1 0 30 -15 59 4 -2 -13 -37 14 -33 -15 -1 -7 9 2 -5 -9 -6 18 -20 6 -21 16 13 -11 3 10 1 2 6 16 5 0 2 -9 9 5 -1 -2 -5 4 -7 4 0 2 -1 -3 3 -2 0 -3 4 -5 1 -7 2 3 1 5 2 -5
  -47 -80 -6 -13 52 -1 43 18 -31 -57 -19 15 -35 -40 34 -30 -12 -47 36 -47 -76 -8 15 16 -23 31 -12 53 11 23 17 -23 -4 4 -10 -33 -4 -16 16 23 -19 -11 1 -2 -18 -1 -14 -11 -7 4 12 -6 6 -5 4 -6 -2 3 1 -3 -4 -16 1 3 0 2 1 7 -4 -1 -6 -3 10 3 -9 0 2 -7 7 4 1 -4 -1 5 -1 -2 -4 0
  121 190 189 5 -45 -41 -45 -19 -27 90 -23 -23 -62 -69 -71 -44 21 29 -112 86 88 4 -51 -102 -64 -43 19 -35 -24 -68 -2 1 30 -18 23 40 20 46 -13 -14 22 9 -15 3 -21 16 -18 17 -1 -15 -22 -8 -16 -2 7 -12 -4 -6 0 -4 -8 2 7 -9 -4 -1 -2 -3 -4 -5 -7 -2 -3 -1 3 -3 -4 5 -4 -2 3 3 0 3 -5 -3 -2 4
  194 217 97 -21 -26 -57 -56 30 -30 16 -12 -4 -128 -59 -87 10 -57 -2 -88 25 29 18 -19 -19 -30 -51 20 -7 18 -43 55 -5 4 -16 -1 20 -25 10 -11 -23 28 1 -15 -19 -24 28 -24 15 -17 9 -2 -13 -12 3 -1 -11 -5 10 1 9 1 -5 3 3 -2 5 -5 4 -8 -3 -8 -4 5 2 -2 -10 -6 1 5 -4 -2 -3 4 3 -1 -3 -4 1
  31 22 3 27 -75 -23 13 -51 5 6 24 -25 4 -9 -16 -2 11 20 -11 4 28 -20 16 -8 21 -3 17 -45 -11 -8 -11 10 6 -1 23 19 -3 23 -16 -23 12 15 8 -14 -2 -8 3 10 4 -6 -17 -4 -11 6 -1 0 -6 -6 -12 0 0 6 1 2 6 6 5 -3 -2 -1 -2 0 0 -4 1 -2 1 -1 -3 3 0 0 6 4 -3 1 -6 4
  -2 -7 -159 38 23 28 -58 -5 -9 -55 2 -37 44 32 10 68 -10 -49 79 -50 -21 9 7 78 34 8 6 15 -2 17 17 -12 -24 16 -5 -10 -3 -5 -2 -20 27 5 0 -16 7 -6 7 8 4 11 5 4 1 -2 -1 0 -7 6 -1 14 6 7 -7 -6 -4 0 0 7 -1 -2 0 -3 1 -2 1 -2 -2 1 1 -2 -2 -3 -1 -4 2 1 2 -1
  -50 -108 29 10 44 15 68 15 -18 -23 18 51 20 -6 29 -20 5 17 26 -26 -35 -9 23 3 8 27 2 11 4 28 -20 7 2 9 -13 -8 -12 -27 7 29 -43 -6 0 23 3 3 3 -20 -3 1 13 8 3 2 -14 7 8 0 6 -3 7 -9 8 15 3 4 -4 -1 3 3 -3 -2 5 4 -7 -3 -3 0 0 0 -3 3 2 2 2 1 -1 1
  203 239 113 -10 -39 -30 -94 28 -18 57 3 -1 -70 -17 -114 40 -45 56 -111 61 94 44 -35 -25 -5 -88 28 -45 10 -44 29 24 7 -12 -16 50 -27 2 -15 -24 22 14 -17 -1 1 23 -10 15 -13 13 0 0 -11 9 -6 4 9 12 4 11 10 6 10 4 -5 0 -7 -3 -4 2 -1 -1 -3 -4 2 -7 -8 5 -2 -8 -2 -1 3 1 -1 2 2 -1
  -261 -303 -61 21 166 97 99 25 -31 -30 -21 67 147 25 139 -48 67 -33 135 -52 -99 -18 3 2 -23 109 -29 76 -23 55 -61 -20 -5 26 -13 -50 55 -39 12 65 -63 -28 5 51 9 -12 14 -39 19 -17 19 24 23 -16 -6 1 16 -5 19 -4 0 -9 0 1 -1 1 -4 0 5 -2 -2 -3 2 8 -4 -3 0 2 -1 1 3 3 -8 -3 1 0 5 -1
  5 18 -56 35 -29 -3 -32 -32 15 0 0 -40 32 15 6 24 17 -19 21 0 26 -5 -7 20 20 2 9 -22 -15 -9 2 -8 -6 2 19 11 11 22 -6 -26 31 12 1 -15 8 -7 8 11 9 -1 -14 1 -5 -4 2 -1 -8 -7 -7 7 0 15 -5 -8 -2 5 7 0 4 -1 2 0 -7 -3 3 2 1 4 -2 3 -3 0 0 -5 -1 0 2 4
  375 506 257 -106 -93 -112 -180 63 4 142 -59 -30 -243 -69 -207 12 -95 64 -263 141 147 63 -80 -104 -85 -163 25 -36 28 -112 94 9 26 -50 -5 62 -6 43 -26 -41 68 12 -19 -24 -30 42 -50 30 -20 12 -16 -28 -16 4 23 -11 -3 19 -5 3 -2 8 6 -12 -8 -9 -8 -1 -15 -6 -1 4 -4 -7 6 -4 -4 2 2 -5 4 -4 2 4 1 -3 0 -1
  -165 -227 68 88 168 83 71 19 -81 -11 -15 64 130 -26 85 -62 75 -29 92 -31 -54 -12 -10 -56 -43 96 -1 54 -25 17 -85 -5 13 25 11 -30 27 -19 18 61 -67 -31 -18 52 -6 3 20 -27 5 -23 14 24 7 -11 -15 -5 10 -11 24 -6 -1 -16 3 11 -2 -2 -9 0 9 -1 -8 -9 9 12 -12 -8 -7 6 -1 -4 -3 10 -5 0 -3 -3 -2 -1
  102 145 208 -61 -48 -34 -1 28 11 93 2 35 -81 -27 -80 -36 -17 91 -146 92 75 23 -28 -85 -32 -70 1 -38 11 -34 -2 30 28 -22 -18 37 -16 -1 -1 9 -17 3 -8 22 0 17 -11 0 -14 -3 1 -2 -3 10 -3 7 15 5 6 -11 0 -7 15 6 0 -7 -8 -7 0 6 1 5 -4 -1 4 0 -3 1 -3 -4 2 3 2 4 -2 2 1 -4
  -60 -96 -202 16 45 31 -14 2 2 -86 -3 -25 47 41 47 58 -19 -67 116 -81 -75 -4 28 96 41 37 -4 41 6 36 23 -23 -33 17 -2 -32 7 -15 1 -9 16 -4 9 -18 6 -12 7 -4 6 13 9 3 9 -6 4 -2 -8 4 -5 15 7 7 -12 -5 0 5 4 8 -2 -3 1 -1 6 -2 -3 -2 2 -2 5 1 -1 -9 0 -3 2 -3 -1 0
  -17 -18 58 -1 79 15 -3 42 -20 16 -30 30 -3 -9 12 -15 -3 -6 -2 8 -16 15 -22 -33 -33 11 -2 39 5 -6 -2 -8 1 0 -2 -11 17 -8 9 25 -17 -16 -11 19 -4 12 -3 -11 -4 -4 7 4 4 -6 0 -4 5 2 11 1 -1 -1 1 1 -5 -6 -6 0 0 -1 -1 -1 3 4 -4 -3 -2 4 1 -4 -1 0 -2 0 1 -3 2 -3
  59 94 -99 33 -130 -34 -41 -98 16 -10 35 -95 1 -4 -22 25 18 -27 17 6 29 -34 9 21 24 -12 19 -46 -29 -28 9 -9 -3 -3 40 18 12 55 -21 -56 62 29 9 -39 -15 -12 -3 35 11 -2 -27 -14 -20 2 10 -11 -25 -5 -24 8 -6 15 -7 -17 3 5 11 1 -9 -8 -3 -1 3 -8 6 0 -1 1 -1 2 8 -3 5 4 -4 -7 -6 7
  237 300 285 -53 -82 -98 -57 22 -23 104 -21 -6 -176 -101 -134 -58 -31 50 -198 110 91 16 -46 -124 -81 -87 20 -36 7 -84 30 11 38 -32 11 46 -12 40 -12 -14 22 4 -22 -3 -36 34 -35 22 -22 -7 -14 -20 -20 6 7 -13 -3 7 0 -9 -11 -11 11 1 -2 -5 -9 -2 -8 -6 -9 -2 3 1 1 -5 -6 1 1 -5 5 2 2 9 -4 -4 -6 -1
  349 434 116 -65 -197 -110 -177 15 85 120 -6 -66 -160 27 -192 76 -100 93 -223 127 179 55 -42 -37 27 -166 32 -106 38 -87 72 41 5 -42 16 81 -39 46 -29 -83 89 26 -6 -50 15 19 -5 42 -17 21 -27 -17 -18 17 17 4 -7 6 -19 9 5 33 -6 -8 -3 -8 5 -10 0 5 18 10 -14 -14 11 4 2 4 -1 -2 -5 -5 7 -2 0 2 2 -2
  -2 -36 -157 39 -53 5 -12 -43 23 -49 35 -37 51 48 8 62 -8 -8 64 -48 -2 -13 38 76 70 6 11 -33 0 24 3 8 -21 12 10 5 -14 3 -13 -32 21 17 14 -25 15 -17 14 8 9 9 -7 1 -5 8 -4 7 -8 -1 -13 10 9 13 -7 1 5 6 7 0 0 0 3 1 -1 -5 2 0 2 -2 -3 1 -3 -3 5 -2 1 3 -3 3
  18 25 153 15 77 20 18 29 -67 30 -15 54 -8 -58 -18 -44 18 19 -39 24 17 14 -28 -68 -57 1 5 14 -7 -19 -20 4 21 0 -11 6 1 -9 4 34 -38 -11 -18 30 -14 17 -9 -10 -6 -9 8 4 -1 1 -10 -4 12 2 18 -5 0 -16 12 9 -2 0 -9 -1 -2 1 -8 -4 3 6 -4 -7 -5 1 -3 -6 0 5 -1 3 -2 1 -1 -1
  -63 -74 -77 -11 62 36 3 23 -8 -28 -11 15 42 31 32 25 -4 -14 55 -35 -36 9 7 43 10 17 -11 29 3 28 9 -6 -15 9 -23 -16 14 -26 -1 13 -12 -4 8 8 6 -7 -2 -16 8 7 12 7 12 -4 1 6 9 6 4 5 8 0 -2 -1 -1 5 0 3 -1 -2 -1 1 0 -1 -1 -2 2 -2 2 -1 1 -5 -3 -2 1 2 2 0
  90 129 -151 38 -261 -58 -49 -131 90 12 74 -128 23 51 -39 60 8 27 -17 39 91 -34 20 52 100 -44 18 -124 -23 -19 -1 22 -12 -3 43 54 -19 61 -30 -95 88 49 17 -53 25 -21 24 56 9 2 -39 -8 -25 16 2 3 -23 -9 -30 10 -5 33 -6 -16 2 0 15 -9 -1 2 11 3 -12 -13 19 6 1 5 -8 3 4 1 7 -1 -4 4 0 5
  -146 -186 -108 -14 -37 13 97 -29 54 -32 37 17 68 53 81 -15 26 10 64 -29 -48 -36 45 43 54 51 -20 -13 -2 47 -30 5 -9 9 1 -17 1 -18 -1 7 -20 -1 19 5 22 -20 21 -9 8 -6 1 7 10 1 -6 10 4 -7 -3 -6 -2 3 -3 6 7 5 6 -5 7 3 8 3 -5 -1 4 5 5 -1 -2 5 1 0 -1 0 2 3 2 0
  -86 -104 -58 -28 54 23 57 20 -8 -45 3 34 9 6 43 -4 -5 -14 50 -44 -64 -5 23 39 6 27 -18 36 8 37 10 -12 -11 8 -27 -26 1 -31 7 24 -28 -7 9 10 1 -4 -6 -17 -1 4 16 1 13 -1 -3 3 7 7 6 -1 2 -11 4 5 3 4 -2 4 -4 1 -3 1 3 2 -1 0 2 -5 2 -1 3 -5 -1 1 2 2 0 -3
  -141 -190 -92 48 47 45 54 -28 -9 -48 4 0 87 16 75 -9 30 -30 101 -57 -60 -25 26 24 20 64 -7 25 -13 36 -37 -8 -10 16 15 -28 18 -2 8 20 -22 -3 11 8 4 -18 15 -12 11 -7 2 6 3 -2 0 1 -4 -7 -6 -3 -1 0 -2 1 5 1 4 0 -1 -1 1 0 7 0 -5 0 1 -1 -1 4 3 1 1 1 -1 -1 -4 3
  113 147 14 -60 -54 -52 -49 21 27 15 -16 -27 -108 -17 -56 9 -55 -6 -66 22 6 10 -8 -1 -10 -45 -2 2 19 -25 50 -9 -2 -19 2 3 -9 14 -3 -21 35 1 0 -22 -11 10 -16 13 -12 8 -1 -16 -2 1 13 -8 -9 7 -9 1 -5 1 -3 -6 0 -3 -1 3 -7 -2 2 3 3 -4 3 0 0 -2 6 1 4 -6 2 1 1 -4 -2 -1
  239 314 133 -40 -61 -66 -120 32 -13 57 -28 -29 -140 -44 -135 30 -62 29 -148 67 100 51 -46 -33 -31 -110 14 -33 21 -60 67 10 8 -25 -15 43 -28 21 -9 -33 42 15 -15 -24 -14 23 -27 25 -18 16 -6 -18 -11 9 8 -2 1 13 -1 3 -2 1 6 -4 -6 -1 -2 0 -9 0 -3 2 -6 -6 4 0 1 -1 1 -6 0 -4 0 1 -1 2 1 -2
  -37 -43 -1 -15 63 24 26 35 -3 -2 -14 36 -2 19 13 12 -21 15 12 -19 -26 11 7 9 2 7 -6 27 17 19 11 0 -8 0 -18 -14 3 -23 3 16 -24 -10 10 10 4 2 -2 -20 -1 2 9 4 9 0 0 4 7 2 4 -2 7 -3 1 4 3 1 -2 2 -1 4 1 5 2 2 -3 -2 1 -2 2 -1 -1 -3 0 1 3 1 -1 -3
  -217 -264 -226 29 44 55 72 -44 15 -94 12 -15 127 42 136 3 50 -72 168 -88 -103 -38 33 83 35 96 -24 41 -25 62 -25 -28 -24 26 7 -45 34 -14 9 14 -8 -1 16 -1 15 -29 16 -11 24 -3 1 8 10 -11 -2 0 -3 -7 -4 9 -1 6 -10 -10 0 6 7 3 1 -3 0 -3 -1 3 2 4 6 -3 -2 6 1 -1 -2 -8 0 0 4 5
  -198 -253 -71 61 191 122 61 33 -67 -60 3 82 152 31 89 2 51 -27 140 -75 -70 5 15 28 -2 79 -10 63 -9 53 -59 -2 -5 32 -29 -43 8 -54 18 62 -74 -28 -5 45 9 -8 23 -37 6 -6 32 25 22 -5 -17 9 16 -1 25 -4 9 -17 3 15 2 0 -7 4 9 4 -1 -4 6 6 -9 -4 -2 1 -1 -5 -4 2 -4 -2 3 3 3 -6
  -149 -196 -26 -4 138 57 53 48 -14 -30 -24 60 76 19 89 -22 26 -32 80 -41 -73 3 -1 11 -17 64 -20 63 -2 36 -23 -17 -6 13 -14 -38 27 -38 18 50 -44 -23 -5 32 8 -3 7 -33 10 -2 19 15 18 -14 -7 4 15 -1 14 2 5 -5 -2 5 -3 5 -2 1 8 1 0 -1 -1 6 -6 -1 2 1 1 2 -4 2 -4 -6 2 -2 5 1
  -37 -55 -8 76 54 40 -19 -18 -39 -5 2 0 73 1 16 5 37 -18 51 -20 8 -3 -4 -12 -7 28 20 6 -18 -3 -39 1 7 12 18 -6 10 9 0 6 -8 -3 -4 7 -6 -5 13 -4 7 -10 -2 9 -5 -4 -3 -1 -4 -7 -1 -1 2 0 -2 3 3 -1 0 2 5 -2 -1 -3 5 1 -7 -2 -4 3 -1 1 -2 5 0 1 0 -2 -2 2
  111 177 222 -3 -9 -40 -48 -3 -41 86 -41 -8 -81 -81 -64 -59 14 17 -121 78 77 14 -57 -118 -89 -40 13 -11 -14 -70 5 -2 35 -26 21 23 20 41 -4 1 12 3 -14 0 -33 15 -26 11 -1 -14 -19 -14 -15 -5 12 -12 -1 -3 -1 -9 -11 -4 6 -7 -4 -1 1 -3 -6 -5 -6 -1 -1 0 -2 0 0 1 -1 1 4 5 -1 4 -5 -4 -4 5
  55 108 179 -52 -11 -39 16 11 -19 59 -32 8 -91 -71 -36 -63 -2 28 -99 63 25 7 -38 -85 -69 -32 -9 6 -7 -35 19 -5 20 -20 -6 17 20 17 3 16 -7 2 -7 14 -19 16 -30 1 -5 -6 -7 -12 -5 -1 7 -8 5 2 4 -6 -9 -7 12 -8 -6 -2 -4 -3 -11 -4 -10 0 0 2 3 -1 1 0 -1 -3 7 0 -1 2 -4 -2 0 1
  -297 -423 -288 29 114 97 133 3 6 -161 38 50 174 78 177 18 30 -77 234 -144 -171 -28 68 140 77 126 -41 70 6 114 -38 -17 -41 43 -25 -72 -6 -71 29 45 -57 -20 11 16 33 -28 37 -30 11 12 34 22 26 -3 -22 11 11 -1 12 9 6 -8 -9 10 3 8 4 2 9 7 4 -3 4 6 -5 2 5 -6 2 1 -4 -2 -3 -7 3 2 5 -4
  -225 -303 -9 65 160 88 117 8 -59 -34 6 82 158 -1 127 -56 83 -17 130 -56 -82 -24 9 -13 -18 115 -7 50 -34 50 -81 -8 4 32 -4 -33 37 -39 11 65 -77 -23 -6 57 8 -6 17 -38 17 -19 15 28 11 -13 -22 1 18 -9 23 1 5 -11 5 11 -1 6 -8 -2 7 -2 -9 -10 3 13 -8 -7 -5 3 -5 -2 -3 8 -5 -4 0 0 3 2
  75 89 -6 5 17 -6 -66 22 -11 -1 -12 -8 -26 1 -41 42 -26 -7 -20 -7 27 29 -12 22 4 -33 10 -4 10 -11 30 -1 -5 -4 -10 8 -15 -4 1 -14 16 6 -5 -13 0 4 -6 3 -3 10 2 -3 -2 0 -1 3 2 6 0 7 6 2 0 1 -2 4 -1 4 0 1 -1 0 -4 -2 -1 0 -1 -2 1 -2 -4 -2 0 -4 1 2 0 0
  97 124 74 -49 31 -16 -38 52 -32 17 -18 38 -67 -22 -50 5 -31 17 -60 21 23 31 -23 -7 -39 -43 2 13 15 -14 41 3 6 -7 -36 10 -6 -20 -11 8 -3 -4 -7 5 -11 19 -24 -5 -7 12 11 -3 4 1 -2 2 13 15 11 3 5 -8 5 3 -3 3 -7 2 -5 -4 -5 -3 -2 2 0 -4 0 -2 2 -5 -1 -3 -3 0 3 3 6 -2
  -105 -118 -173 68 -47 32 2 -86 32 -38 22 -65 116 50 59 30 47 -39 102 -37 -6 -30 21 45 54 43 4 -24 -26 13 -33 -9 -13 13 44 -8 23 32 -4 -29 29 15 14 -26 14 -32 29 13 21 -7 -20 2 -4 -1 6 -1 -15 -16 -20 5 -3 20 -13 -11 6 5 17 -2 4 1 8 4 -4 -8 3 5 6 0 -4 7 1 -1 4 -1 -4 -2 -3 4
  98 145 117 -40 -20 -40 -38 15 -17 39 -20 -3 -80 -46 -50 -20 -9 12 -87 49 43 18 -35 -39 -49 -46 1 -7 -2 -34 32 -2 14 -15 -14 21 1 8 -2 -4 13 7 -10 -3 -15 14 -26 8 -3 4 -5 -9 -7 -3 4 -3 5 6 3 1 -3 -4 6 -6 -7 2 -2 0 -4 -4 -6 -2 -5 2 2 1 0 -1 0 -1 2 0 -3 -1 -2 1 3 2
  -145 -179 -40 31 45 44 85 -20 -10 -19 11 29 90 9 75 -33 46 -1 74 -29 -44 -28 17 0 9 65 -11 13 -19 32 -46 -3 -1 16 5 -16 23 -9 1 27 -35 -7 8 25 11 -10 15 -15 10 -13 2 11 7 -2 -8 1 4 -8 6 -4 -1 -2 3 3 4 2 -1 -3 1 0 -1 -2 1 4 0 -2 -1 1 -4 0 2 3 -1 -1 0 2 0 1
  168 226 208 20 -47 -47 -71 -12 -36 93 -14 -25 -75 -76 -92 -35 8 32 -127 89 96 13 -55 -105 -61 -54 30 -39 -20 -74 -3 6 33 -20 24 43 4 43 -9 -19 26 11 -21 3 -24 21 -17 21 -7 -13 -18 -6 -22 -2 3 -12 -4 -3 0 -1 -5 1 9 -5 -7 -4 -5 -2 -3 -3 -6 -4 1 0 0 -5 -10 6 -2 -2 2 6 1 4 -5 -4 -4 4
  76 106 -74 20 -69 -3 -47 -25 24 -1 35 -26 -1 37 -43 65 -19 17 -11 6 53 8 8 45 51 -39 16 -50 6 -9 17 14 -9 -1 -1 23 -32 6 -12 -42 31 15 3 -25 13 -2 13 19 -4 7 -6 -2 -6 11 -6 5 -6 1 -5 6 5 9 -2 2 4 2 3 0 3 6 7 3 -7 -5 7 0 -1 2 -2 -3 -3 -2 4 -1 1 4 2 -2
  -335 -458 -250 131 161 137 117 -46 -47 -134 34 21 261 53 188 6 98 -86 278 -144 -142 -46 53 87 53 164 -9 61 -44 90 -95 -18 -26 55 11 -61 30 -37 22 47 -60 -17 6 32 20 -34 43 -31 26 -12 17 31 13 -13 -19 3 2 -15 10 9 8 -4 -7 6 2 7 1 5 9 -1 -5 -10 9 9 -9 -4 -2 2 -2 1 -3 4 -2 -7 -2 -1 -1 3
  88 125 195 -63 4 -41 -3 44 -6 79 -30 32 -100 -50 -55 -55 -14 40 -115 71 30 9 -30 -96 -70 -35 2 8 8 -43 10 2 25 -20 0 14 16 10 -6 18 -8 -12 -12 18 -19 25 -23 -4 -10 -10 -3 -8 -1 -3 6 -8 4 5 7 -8 -6 -7 6 1 -1 -6 -10 -2 -5 -5 -5 1 3 4 0 -4 -3 3 0 -3 3 1 0 5 1 -4 -1 -3
  -3 32 -150 -29 13 2 -47 10 16 -42 -29 -42 -18 26 16 50 -33 -56 48 -37 -37 9 -2 71 9 -2 -16 39 10 13 58 -28 -27 0 -12 -22 18 1 -5 -20 39 3 14 -26 -2 -5 -12 5 6 13 1 -9 8 -6 15 -5 -8 8 -7 10 0 8 -11 -17 -4 2 5 8 -8 -4 0 3 -1 -3 5 2 7 -3 5 1 3 -8 -3 -5 3 -1 4 1
  -3 -22 -30 -17 37 3 -3 31 -9 -30 -14 13 -16 0 8 4 -24 -25 19 -26 -38 8 4 23 -5 8 -9 34 16 13 18 -8 -8 2 -12 -19 -6 -16 6 9 -4 -12 0 -2 -2 4 -3 -6 -5 10 12 0 8 -3 2 -2 0 5 4 2 1 -5 -4 0 -1 -1 -2 3 -1 0 0 -2 5 2 -4 0 1 -3 6 0 -2 -2 -2 -2 2 -1 1 -2
  137 200 144 47 -77 -33 -66 -42 -27 78 7 -42 -39 -52 -93 -12 19 35 -99 70 110 4 -32 -77 -26 -53 30 -65 -21 -63 -14 17 28 -14 25 46 -11 49 -12 -33 28 17 -10 -9 -17 7 -5 26 -6 -14 -21 -7 -21 7 3 -7 -10 -6 -5 -8 -6 -1 8 -2 1 -4 -1 -1 -1 -1 -4 -2 -2 -3 3 -2 -7 3 -3 -2 3 5 2 4 -6 1 -7 2
  -154 -195 -298 -1 -46 4 61 -64 47 -116 16 -64 64 41 122 18 7 -89 161 -91 -123 -52 46 117 59 82 -25 35 -15 60 17 -39 -41 20 18 -43 32 4 -4 -19 33 8 26 -30 10 -28 7 8 19 7 -7 -4 5 -8 10 -9 -17 -4 -18 16 -6 16 -16 -19 -1 7 13 3 -9 -7 1 -3 4 -2 5 3 8 -4 3 8 6 -9 -1 -3 0 -4 2 6
  186 270 187 -28 -198 -82 -42 -46 51 106 35 -43 -111 -21 -134 -10 -14 103 -193 117 159 10 -14 -75 10 -118 14 -117 9 -61 8 47 33 -33 6 68 -54 45 -7 -49 30 29 2 -24 2 3 -3 33 -18 -3 -24 -17 -19 23 6 7 -6 -7 -13 -22 -8 0 9 1 4 -9 6 -8 5 11 9 10 -12 -9 11 13 3 -2 -5 0 1 5 4 5 -3 7 -3 -2
  -141 -223 -201 99 55 71 25 -44 -16 -88 38 -5 165 54 90 42 50 -54 165 -90 -55 -24 36 83 61 82 9 4 -25 46 -51 -6 -20 32 17 -24 2 -17 4 1 -11 0 1 0 18 -23 34 -7 20 0 4 20 1 -7 -15 6 -2 -10 0 14 10 8 -9 5 2 11 6 1 10 0 2 -6 2 2 -6 -2 -3 2 -3 3 -7 2 0 -6 0 -1 -1 4
  73 61 -210 -13 -190 -59 -38 -65 94 -40 40 -99 -5 63 -14 75 -45 -5 20 -15 14 -18 35 100 105 -27 3 -68 7 13 40 5 -34 1 25 24 -15 27 -25 -77 76 31 20 -56 28 -20 15 34 5 18 -21 -8 -9 12 7 2 -15 -1 -28 19 2 31 -14 -12 2 6 15 -5 -3 1 11 4 -8 -13 13 3 8 -2 -1 4 0 -10 7 -3 -2 2 0 4
  60 111 -97 19 -121 -34 -58 -66 41 24 15 -87 10 19 -18 29 11 -16 1 28 43 -24 -7 17 26 -11 12 -46 -22 -29 9 -9 -8 -3 38 23 25 51 -30 -60 73 21 9 -32 1 -5 5 34 11 -6 -27 -5 -12 -1 10 -11 -20 -4 -17 10 -6 23 -10 -19 0 0 7 -1 -5 -7 2 -1 -5 -6 12 -2 -2 6 -2 2 5 -1 2 -1 -2 -2 0 4
  -63 -98 -163 22 -6 41 18 -14 28 -57 42 5 69 74 30 67 -10 7 78 -55 -19 -1 43 93 80 11 1 -16 11 46 -4 15 -23 14 -19 -7 -29 -31 0 -10 -7 7 16 -8 27 -16 24 -6 3 12 10 9 8 7 -11 17 3 1 -4 5 12 6 -2 9 6 5 4 1 6 7 8 3 -3 -4 1 2 1 0 0 1 -4 -2 3 -3 4 6 3 -1
  251 339 164 -49 -69 -72 -118 26 -11 90 -40 -38 -145 -57 -132 6 -56 32 -157 94 95 37 -61 -71 -57 -99 20 -24 8 -77 59 1 14 -28 5 46 7 39 -23 -35 54 11 -14 -16 -23 29 -32 25 -12 6 -14 -16 -14 4 15 -13 -4 10 -5 7 -3 8 3 -13 -7 -4 -4 -1 -13 -5 -5 1 0 -6 5 -7 -3 3 2 -5 4 -4 2 4 -3 -4 0 1
  59 55 47 -62 -100 -63 50 3 48 10 21 8 -99 -9 -23 -22 -46 38 -71 22 -3 -14 24 -5 19 -25 -8 -27 27 2 27 13 2 -17 -3 7 -31 -2 -4 -12 3 2 10 -14 0 6 -7 6 -14 4 -2 -13 -3 12 -1 1 -1 3 -8 -8 -5 -5 3 8 7 0 1 -4 -3 4 3 4 0 -1 4 1 4 -3 4 3 1 -1 5 5 0 2 -2 0
  -206 -270 -230 66 73 76 39 -37 -5 -98 21 -18 154 58 118 28 49 -77 187 -98 -93 -29 37 89 46 89 -12 42 -22 59 -36 -19 -25 31 6 -46 21 -16 15 13 -13 -4 12 1 11 -30 24 -13 19 0 10 13 9 -9 -2 3 -6 -7 -4 6 3 2 -11 -4 2 4 7 5 6 -2 2 -2 5 1 -5 3 2 -1 3 4 1 -2 -2 -4 0 -2 0 2
  -202 -239 53 -40 109 42 141 31 -16 -18 -4 85 42 -10 108 -86 47 -6 50 -17 -95 -24 13 -31 -42 76 -34 63 -5 39 -38 -10 10 8 -22 -42 24 -42 23 70 -74 -28 0 45 -4 -1 -3 -34 4 -14 18 9 16 -10 -8 1 18 -1 19 -12 -5 -22 5 8 0 0 -6 -1 4 -1 -4 -1 3 13 -4 1 2 -1 1 0 4 4 -6 2 -1 -1 3 -3
  97 126 20 -49 -41 -30 -32 18 12 5 -7 -6 -86 -9 -58 24 -52 26 -65 17 22 24 -6 14 6 -57 1 -11 19 -7 46 4 -4 -13 -22 15 -22 -7 -1 -13 14 10 2 -13 2 6 -14 6 -12 14 3 -9 0 6 6 4 3 8 -3 3 3 2 6 -1 -3 -1 0 1 -7 3 3 3 -1 -5 2 1 1 -3 1 0 1 -7 1 2 1 3 1 -3
  -65 -114 3 47 52 36 27 5 -17 -14 8 29 68 10 37 -10 22 -6 44 -17 -21 -4 5 -7 11 38 4 8 -4 13 -44 7 1 11 11 -10 -6 -13 12 21 -28 -12 -11 19 8 -2 21 -9 0 -5 8 14 1 -1 -11 3 5 -6 8 0 3 -2 0 10 0 -1 -2 -3 9 3 3 -3 3 3 -7 -3 -4 4 -1 0 -5 5 0 0 -2 -2 -1 0
  133 201 111 -58 -70 -70 -39 -3 10 51 -24 -32 -137 -45 -68 -23 -30 6 -107 57 40 -1 -20 -60 -53 -53 6 -5 10 -56 50 -7 15 -29 15 12 8 38 -11 -22 35 2 1 -27 -32 14 -31 17 -7 -2 -18 -26 -10 -1 20 -14 -14 2 -11 -7 -11 -1 -4 -10 1 -2 3 1 -10 -7 -3 4 2 -2 2 2 5 -1 5 1 6 -3 2 7 0 -6 -4 1
  271 314 273 -61 -58 -73 -84 53 -13 113 -8 28 -149 -55 -163 -11 -50 97 -210 110 124 44 -42 -98 -51 -118 31 -54 19 -71 29 33 35 -28 -15 62 -31 9 -15 -11 7 6 -22 8 -12 34 -26 8 -21 7 -3 -7 -12 8 0 2 10 10 6 -2 8 -3 13 9 -3 -5 -12 -4 -1 1 -2 0 -2 0 -1 -4 -8 1 -2 -6 -4 1 3 4 1 1 -1 -3
  -74 -88 106 -22 84 5 43 36 -15 18 -45 34 -2 -32 54 -70 24 -25 -4 17 -41 1 -31 -64 -63 40 -20 54 -5 -8 -12 -20 10 -6 9 -22 37 -4 20 42 -27 -21 -15 24 -10 9 -8 -16 4 -9 2 1 5 -15 2 -8 9 -6 11 -2 -9 -4 -2 -4 -8 1 0 -4 2 -3 -4 -1 0 7 -5 0 3 3 2 0 0 4 -5 -2 -2 -7 3 1
  -77 -114 -210 39 -125 3 25 -90 68 -57 61 -73 92 66 42 43 21 -11 85 -39 -11 -35 48 84 103 23 -5 -56 -14 35 -26 10 -22 14 25 5 -16 15 0 -41 29 24 17 -28 31 -33 33 20 10 5 -12 3 -4 9 -2 7 -12 -12 -19 6 0 18 -9 -6 4 2 13 -4 4 5 9 2 -5 -8 8 8 4 -2 -4 4 0 -2 4 -4 -3 2 -2 2
  -183 -247 -186 50 73 66 40 -11 15 -75 10 -5 122 65 104 26 27 -59 152 -85 -89 -21 39 70 48 82 -10 42 -4 53 -36 -12 -22 22 11 -47 8 -21 18 13 -16 -15 11 1 14 -24 29 -17 12 -2 10 14 12 -10 -1 3 -5 -9 -3 2 4 2 -14 1 3 0 4 5 10 2 5 0 5 2 -6 3 2 0 5 5 -4 1 -2 -4 1 -3 -1 0
  61 52 29 -1 -8 -2 -43 28 22 19 4 1 -13 32 -44 37 -31 27 -39 18 37 26 -2 2 27 -39 7 -21 21 -10 3 23 -3 -7 -4 14 -31 -8 10 -8 2 -2 -8 -3 14 4 13 1 -10 10 6 4 0 6 -2 9 4 0 0 0 7 4 -2 7 0 -4 -1 -2 8 6 8 5 -2 -2 -2 2 -1 3 2 -2 -6 0 1 -2 0 0 0 -3
  124 149 225 -12 6 -26 -24 48 -32 76 -2 47 -83 -48 -89 -30 -19 62 -125 65 68 28 -24 -83 -42 -57 17 -22 16 -38 -5 25 30 -15 -16 27 -35 -5 3 11 -24 -8 -17 20 -15 24 -10 -2 -23 -6 9 0 -5 8 -7 2 8 5 12 -15 -1 -19 14 17 1 -7 -11 -1 5 5 -2 0 2 2 -4 -3 -8 1 2 -5 -1 5 0 7 0 2 -3 -6
  67 65 92 -21 49 -21 -2 55 -35 -3 -22 28 -87 -53 -32 -17 -41 -12 -40 -2 -22 16 -9 -16 -33 -14 -1 32 20 -8 32 -11 2 -7 -18 -7 -19 -13 10 15 -12 -11 -11 7 -19 21 -19 -6 -19 4 16 -6 1 1 -2 -6 1 9 8 -3 -2 -17 8 9 -2 0 -7 6 -4 0 -7 -2 8 4 -5 -6 -5 -1 7 -3 1 -2 0 3 0 -1 -3 -2
  56 62 -30 -51 -158 -70 12 -53 64 25 34 -46 -27 4 -13 -15 9 29 -42 38 26 -35 15 6 24 -16 3 -61 -19 -9 6 4 4 -5 18 32 15 27 -30 -36 40 24 10 -15 7 -5 -8 19 12 -1 -23 -7 -10 0 3 -1 -5 -1 -16 7 -2 16 -2 -9 1 7 3 -6 -4 -8 -2 -2 -8 -3 12 1 1 0 -6 4 4 0 2 -1 0 0 2 7
  12 0 53 -27 20 -28 27 16 -16 -9 -24 3 -54 -49 16 -40 -11 -31 -11 -1 -45 -9 -11 -23 -38 20 -9 32 -1 -9 21 -23 -1 -7 8 -11 17 2 6 11 0 -7 -9 1 -18 11 -19 -2 -1 -1 -1 -7 -3 -8 2 -12 0 1 2 7 -5 -4 0 -4 -5 6 0 1 -7 -6 -9 -4 5 5 -3 -6 -1 0 4 0 2 -3 0 1 -4 -6 -3 4
  88 88
  45 59 -7 -38 -77 -24 8 -1 55 7 20 -6 -55 26 -28 23 -43 37 -50 19 24 7 15 20 40 -43 -8 -31 28 5 26 16 -5 -14 -10 11 -35 -3 4 -18 10 10 11 -17 13 -3 4 7 -12 8 1 -8 0 14 1 9 0 2 -9 -5 1 4 3 5 4 -5 6 -2 2 11 12 10 -5 -5 7 5 4 -2 0 2 0 -1 6 2 2 4 1 -2
  84 108 -19 -1 -142 -57 -18 -69 21 14 39 -56 -33 -10 -43 -4 11 11 -34 34 40 -33 11 -8 12 -25 15 -52 -15 -30 3 7 6 -6 26 27 -2 42 -21 -41 43 16 2 -25 -8 1 -2 31 0 1 -21 -11 -15 5 5 -8 -20 -4 -12 0 -8 9 -3 -10 2 -2 3 -4 -6 -9 -2 -5 2 -3 5 2 -3 2 0 0 4 -1 2 4 -1 -2 -4 1
  -237 -280 -404 91 38 86 29 -85 -6 -147 22 -73 194 70 143 65 58 -124 270 -145 -123 -48 55 150 72 116 -12 47 -35 74 -21 -40 -46 47 19 -56 41 3 -7 -18 22 3 27 -26 10 -43 27 3 29 0 -2 9 12 -9 4 -6 -21 -7 -11 15 -2 10 -20 -18 3 8 11 10 -3 -7 -5 -5 5 -4 2 -1 7 -4 3 5 4 -7 0 -4 0 0 -1 1
  226 292 158 36 -99 -42 -134 -5 12 108 7 -46 -49 -2 -130 33 -23 64 -143 112 163 39 -56 -69 0 -102 35 -82 5 -77 4 39 17 -20 19 66 -28 44 -13 -51 53 16 -19 -15 6 19 10 34 -15 2 -16 1 -21 15 3 -2 -4 -2 -5 -1 1 16 2 -3 -5 -13 2 -7 7 7 13 2 -8 -6 6 1 -6 10 -2 -6 -3 5 3 1 -4 2 2 0
  225 255 221 -116 -162 -146 14 11 37 65 -4 -4 -238 -92 -107 -71 -70 56 -203 94 35 -7 -13 -82 -45 -80 3 -35 28 -54 61 2 24 -41 11 37 -24 30 -8 -21 29 9 -9 -18 -24 32 -39 23 -26 7 -15 -27 -17 7 6 -11 -7 7 -9 -3 -11 -2 10 -1 -1 -4 -3 -6 -14 -4 -5 -2 3 1 3 -2 -3 -3 3 1 2 -1 5 8 -1 -6 -5 0
  -136 -148 -182 46 51 73 -3 -31 -3 -51 6 -17 130 56 78 33 43 -51 130 -49 -40 -14 9 55 24 55 -8 25 -22 28 -30 -14 -17 22 7 -27 31 -5 -2 5 3 -3 6 1 11 -20 22 -2 20 -4 1 10 8 -7 2 1 -3 -4 0 7 0 9 -10 -8 0 3 6 1 4 -2 6 1 1 -3 1 1 2 4 -2 2 3 -2 -2 -2 1 -1 4 0
  104 121 188 -34 37 -32 -6 65 -16 55 -26 43 -109 -43 -53 -24 -49 42 -107 47 25 27 -29 -66 -44 -39 5 11 24 -28 27 10 12 -21 -16 11 -16 -11 8 17 -17 -11 -11 15 -11 28 -21 -9 -17 0 8 -4 -5 2 0 -3 8 7 10 -4 3 -8 11 8 -4 -7 -9 0 -3 3 -1 2 4 7 -3 -4 -5 3 4 -4 -2 2 1 1 0 0 -1 0
  -17 -14 35 44 120 49 -46 39 -65 -5 -37 16 32 -21 11 -4 10 -44 30 -10 -13 23 -35 -22 -46 23 1 49 -5 -12 -14 -11 2 7 -6 -19 10 -10 11 24 -11 -18 -17 15 -15 10 2 -5 -1 -5 12 7 2 -10 3 -6 4 3 14 1 -3 -9 0 0 -6 -2 -4 5 2 -2 -1 -5 8 4 -8 -5 -6 5 5 -4 2 2 -7 0 -2 -2 1 -1
  266 338 198 -28 -153 -111 -103 -13 29 113 -16 -65 -140 -61 -122 -23 -39 37 -181 132 118 18 -69 -99 -39 -96 23 -61 -1 -96 42 7 19 -35 43 62 4 69 -13 -53 74 17 -24 -23 -12 27 -19 42 -14 4 -27 -16 -27 8 11 -20 -12 -2 -10 7 -10 21 0 -17 -11 -9 4 -10 -6 -2 3 -2 -6 -5 7 -3 -5 7 1 -2 2 2 6 1 -8 -8 -1 4
  -343 -424 -210 28 149 130 157 -11 -20 -107 45 90 202 74 164 6 76 -15 207 -118 -131 -32 66 97 52 117 -24 47 -23 110 -73 -6 -18 43 -41 -54 16 -80 16 65 -93 -12 18 47 29 -33 27 -48 23 -8 29 30 27 -8 -25 23 22 -1 17 2 15 -14 6 16 8 11 -6 3 8 2 -3 0 1 7 -5 0 0 -5 -8 2 -1 -3 -4 -2 2 7 4 -5
  -220 -281 -279 79 125 99 26 -24 -44 -113 -9 -17 185 43 130 38 49 -100 231 -122 -126 -22 24 104 33 114 -12 71 -34 69 -33 -39 -38 46 4 -50 52 -22 0 16 -11 -9 8 12 11 -25 20 -15 26 -1 12 22 15 -15 -5 -4 -3 -1 6 20 5 5 -11 -12 -4 8 0 6 -3 -8 -8 -9 8 0 -5 -9 -1 -1 1 0 2 -7 -4 -5 -2 -2 0 -1
  93 129 112 0 35 7 -76 40 -17 47 -32 5 -43 -10 -61 16 -25 22 -73 38 65 43 -36 -46 -31 -53 11 2 16 -35 14 13 13 -13 -7 11 -13 5 6 3 2 -4 -9 -1 -6 9 -4 0 -10 1 2 -5 -2 3 7 2 6 3 0 -7 1 -2 3 4 -1 -7 -1 1 4 8 8 7 -3 -4 -2 2 3 2 0 -1 -1 2 2 2 2 1 1 0
  -116 -117 -175 65 -9 18 21 -78 -9 -56 1 -65 86 4 79 1 52 -82 127 -59 -57 -46 17 41 12 77 -5 18 -36 13 -15 -32 -17 16 40 -25 40 34 -7 -20 28 2 12 -22 -10 -20 6 13 22 -9 -18 -2 -3 -10 8 -16 -23 -13 -8 6 -10 8 -15 -20 -1 5 8 3 -7 -11 -10 -8 3 1 2 0 3 -1 2 3 2 0 -2 -4 -4 -4 -4 5
  -147 -215 -270 24 -45 32 94 -62 36 -120 87 -6 103 79 86 49 26 -25 153 -98 -74 -51 89 134 99 57 -7 -15 -1 75 -15 9 -26 29 -15 -27 -30 -31 -3 -11 -12 6 26 -18 24 -27 26 -4 9 10 8 6 9 9 -14 11 -8 -4 -6 2 9 -2 -10 7 11 7 5 5 7 1 2 0 2 3 3 7 6 -5 2 3 -5 -3 2 -2 5 7 2 -1
  -56 -77 -266 -3 -186 -27 34 -103 100 -70 65 -85 39 76 37 48 -1 -15 75 -43 -21 -52 71 111 111 12 -13 -58 2 40 6 2 -28 7 23 0 -18 25 -15 -57 50 29 34 -51 24 -34 25 28 9 9 -20 -11 -3 11 7 8 -23 -8 -30 1 -6 20 -12 -8 10 4 20 -3 0 2 13 6 -5 -11 12 11 8 -4 -3 8 5 -4 5 1 4 3 -2 1
  -19 -14 -39 -31 57 1 1 37 1 -38 -47 -13 -64 -13 16 14 -47 -42 19 -49 -58 12 10 28 -12 8 -17 56 25 17 51 -24 -16 -6 -14 -34 0 -9 12 8 0 -7 16 -18 -14 -4 -19 -12 -5 3 5 -16 8 -6 17 -2 -4 5 -7 -3 -3 -7 -2 -2 0 1 3 11 -7 3 -2 7 4 -1 -2 1 8 -6 7 4 4 -5 2 0 4 1 -4 2
  197 251 160 -66 -170 -76 -39 -12 57 85 57 4 -117 1 -121 -4 -29 98 -179 116 128 11 -11 -52 8 -115 16 -94 20 -54 15 46 30 -32 -11 56 -56 16 -7 -30 24 19 -9 -12 3 16 -2 25 -21 9 -6 -13 -14 19 -2 11 1 3 -7 -13 -2 3 10 10 5 -7 2 -8 7 7 14 6 -7 -5 7 9 -4 4 -2 0 1 3 4 6 2 2 4 -2
  -117 -125 -189 73 -30 46 9 -72 16 -50 22 -56 118 47 62 31 43 -46 117 -43 -24 -30 24 58 55 54 -3 -10 -20 24 -37 -11 -19 20 29 -13 13 20 -6 -26 25 7 12 -18 12 -24 33 16 12 -8 -11 9 1 -1 2 -1 -15 -11 -10 3 -6 12 -9 -8 3 1 12 1 4 2 7 0 -1 -6 5 1 1 3 -3 3 3 0 0 1 -2 0 -2 -1
  -176 -206 -87 14 145 91 47 31 -38 -62 -11 49 92 22 73 11 26 -35 109 -76 -77 10 21 44 3 53 -19 60 0 52 -25 -13 -8 23 -30 -44 4 -45 22 47 -57 -16 4 24 3 -18 9 -30 4 -4 26 10 20 -4 -7 10 14 5 11 -5 4 -20 4 11 5 3 -4 8 5 6 -2 5 1 1 -5 -1 4 -7 -1 0 2 -2 -1 1 0 4 -1 -6
  369 447 496 -96 -31 -105 -106 127 -7 177 -62 52 -286 -98 -222 -43 -115 129 -346 167 170 86 -79 -176 -93 -175 18 -39 66 -104 64 43 49 -62 -26 65 -64 12 10 4 -2 -4 -28 9 -24 55 -38 3 -49 5 5 -21 -13 16 8 4 17 12 5 -23 0 -15 23 20 -3 -16 -10 -4 1 15 9 12 -3 -2 -2 0 -4 3 3 -6 -4 6 5 8 3 2 -2 -1
  18 4 274 -43 139 -18 45 102 -44 78 -81 77 -86 -86 9 -96 -27 25 -84 49 -38 21 -57 -124 -100 19 -7 71 6 -21 6 -20 15 -16 -3 -7 45 -15 14 60 -47 -28 -19 56 -17 35 -32 -35 -8 -13 11 7 2 -16 1 -14 18 2 20 0 1 -7 14 3 -14 -4 -14 -3 -6 -1 -9 -3 8 10 -10 -13 -9 6 3 -2 2 2 -1 0 -2 -8 -2 5
  196 226 190 -50 -31 -42 -79 68 26 98 -2 37 -98 13 -126 30 -62 106 -170 83 126 55 -27 -50 0 -115 17 -58 33 -40 29 46 18 -26 -29 51 -42 -10 -4 -6 -4 9 -9 9 15 21 -9 -4 -16 12 6 -4 -5 15 -3 15 16 9 2 -8 13 2 10 15 2 -5 -7 -7 6 8 11 11 -9 -3 2 5 0 2 -4 -5 -6 1 2 -2 5 6 4 -1
  294 370 356 -84 -70 -104 -98 65 8 154 -49 10 -220 -69 -174 -39 -70 103 -272 141 148 45 -57 -147 -80 -134 19 -46 33 -96 48 31 39 -51 -3 59 -22 33 -11 -9 19 4 -15 -2 -22 39 -36 11 -24 0 -16 -24 -16 5 17 -1 4 6 -3 -17 -4 -1 12 5 -3 -10 -7 -7 -5 0 5 7 -3 -3 0 4 -2 5 -1 -4 1 3 1 6 5 1 -3 3
  -29 -46 -169 55 -75 10 3 -70 3 -54 51 -46 79 28 23 38 21 -24 85 -34 -12 -27 24 73 62 22 8 -33 -20 23 -14 0 -19 20 11 8 -4 9 -14 -36 28 17 7 -17 13 -15 19 20 6 6 -3 9 -4 7 -9 0 -11 -3 -6 13 2 11 -3 -6 1 3 5 -1 -2 -3 -1 -7 1 -4 4 -4 -4 0 0 0 1 -4 2 0 -4 2 0 0
  -15 1 -35 21 40 30 -54 8 -4 19 -22 -15 48 22 5 20 8 -13 29 4 6 15 -24 -4 -8 4 5 19 -10 -6 -11 -9 -5 6 9 -4 32 9 -5 -2 15 -2 -2 7 3 -2 6 -1 8 -2 0 9 3 -7 6 -3 -1 2 -1 6 1 11 -3 -9 -3 -5 0 0 -1 -1 3 0 1 -4 0 -3 -3 4 -1 0 3 -1 -1 -1 1 -5 2 -1
  -86 -88 23 -24 37 22 71 -8 -23 -7 8 40 16 -14 33 -37 31 16 20 -4 -36 -19 10 -20 -23 23 -5 22 -15 14 -18 -5 10 5 -13 -11 21 -15 4 34 -40 -7 1 26 -4 -2 -7 -17 3 -7 7 2 7 -4 -4 1 6 -2 8 -6 0 -9 8 2 1 1 -7 -1 -3 -4 -5 0 4 2 -3 -1 0 -1 -2 1 4 -4 1 5 0 0 -1 -2
  -14 -18 115 4 79 17 19 38 -34 21 -11 58 1 -27 2 -33 12 11 -26 13 6 20 -23 -43 -36 1 -2 16 1 -6 -14 5 16 -4 -13 -4 -6 -19 18 34 -38 -11 -15 26 -4 9 -5 -17 -5 -3 13 5 3 0 -9 1 14 0 16 -5 2 -12 6 9 -2 0 -5 -1 4 3 -4 -2 -1 6 -6 0 -2 -1 0 -3 -4 5 -3 -3 -2 -1 3 -2
  -123 -183 -118 68 162 86 -7 43 -42 -51 -26 25 132 38 81 37 10 -50 140 -74 -72 17 -6 53 15 71 -2 65 -7 46 -23 -16 -28 30 -8 -33 29 -36 8 26 -23 -19 -4 26 17 -5 18 -26 12 4 22 28 14 -11 -10 0 10 2 14 16 14 5 -5 0 -8 0 -4 4 5 1 0 -6 4 4 -7 -10 -4 3 3 -2 -5 -1 -2 -7 0 0 3 1
  -24 -8 -14 9 -26 -3 12 -37 -8 4 16 -12 20 -10 4 -13 30 -7 12 9 -3 -19 -1 -8 -3 8 2 -11 -22 -9 -14 -8 4 1 12 5 15 15 0 -5 3 5 -4 4 -6 -4 -2 7 5 -4 -4 0 -4 -2 -1 -4 -7 -4 1 1 -4 1 2 -6 0 2 0 -2 -3 -6 -6 -3 1 -1 -1 -1 -5 0 -1 0 4 -2 -1 1 -5 -4 -4 -2
  -5 -14 -27 -23 -36 -47 56 -27 -10 -43 -2 -23 -65 -60 32 -50 -6 -51 25 -23 -78 -40 12 0 -29 38 -8 36 -8 2 27 -32 -4 -1 17 -22 18 19 -2 -2 15 -4 4 -14 -25 7 -21 9 -2 -1 -7 -15 -6 -6 7 -21 -18 -1 -4 4 -13 -5 -3 -12 -2 1 0 4 -14 -10 -12 -9 13 5 -1 -4 -1 -3 8 2 6 -3 1 3 -1 -7 -4 3
  -199 -211 -90 19 104 67 75 -15 -35 -46 -7 26 105 4 105 -32 69 -55 124 -59 -82 -30 16 16 -26 87 -21 56 -29 35 -36 -25 -1 20 -4 -44 41 -15 6 40 -38 -17 7 22 -11 -16 0 -22 21 -13 7 6 15 -12 -1 -4 2 -6 10 -6 -5 -14 -6 -4 2 7 -2 5 0 -7 -12 -4 3 5 -2 0 4 -3 1 2 2 2 -5 -2 -1 -1 1 2
  203 228 248 -118 -66 -100 -15 54 -12 60 -12 49 -200 -86 -113 -66 -51 54 -194 78 46 19 -20 -84 -76 -84 3 -14 29 -50 45 13 38 -34 -21 25 -32 -2 -4 13 -7 -3 -17 0 -30 31 -41 6 -22 10 3 -23 -7 4 1 -1 9 15 3 -10 -6 -20 12 11 4 0 -10 -3 -8 -7 -7 -2 2 4 -3 0 -1 -7 3 -1 0 2 -2 8 2 -2 -1 -2
  -48 -48 -226 -30 -106 -43 39 -80 24 -100 21 -84 -35 -14 46 4 -4 -85 89 -69 -102 -59 51 85 25 42 -14 20 -11 24 41 -41 -24 7 21 -31 16 25 -11 -36 47 13 23 -50 -20 -19 -15 25 7 5 -15 -23 -3 -6 16 -15 -29 2 -20 10 -14 2 -11 -20 4 6 8 9 -18 -14 -10 -5 10 -2 4 0 4 -9 7 6 11 -11 2 5 -2 -4 -8 1
  147 189 246 -77 -95 -95 14 1 14 106 -14 14 -155 -70 -82 -79 -16 79 -176 104 60 -16 -21 -124 -66 -53 16 -35 0 -61 10 9 35 -35 18 38 15 32 -20 0 7 4 -5 9 -22 27 -31 8 -8 -13 -24 -15 -15 -5 9 -7 -3 -1 -5 -8 -7 3 12 0 0 -3 -8 -8 -10 -10 -5 0 4 2 0 -2 -7 6 -4 2 4 1 1 9 2 -6 -5 4
  -43 -67 -73 -15 16 -1 37 -5 -14 -51 4 4 -16 -10 31 -14 1 -39 54 -50 -66 -33 37 26 -14 40 -6 38 4 20 7 -17 -3 7 -4 -33 5 -5 -9 11 -6 -12 14 -8 -22 -1 -10 -6 3 -2 3 -9 6 -7 8 -5 -13 2 -4 -7 -5 -12 -5 2 7 3 -2 8 -5 -8 -6 -3 13 3 -4 0 1 -3 7 4 3 -2 -1 5 7 -1 -4 2
  4 -4 -91 31 -48 2 -23 -53 -10 -37 34 -33 44 9 -6 25 26 -19 40 -19 8 -12 13 35 23 1 10 -24 -20 -1 -11 3 -3 11 11 8 -8 12 -2 -19 15 10 -6 -15 2 -10 8 17 7 8 -5 -1 -8 3 -5 -1 -9 -2 -3 6 0 3 -5 -6 0 2 2 -2 -1 -5 -2 -7 -1 -2 0 3 0 -3 -3 -2 -1 -1 0 -2 -3 0 -2 -2
  229 298 111 -21 -126 -65 -120 -10 20 87 -2 -51 -95 -11 -129 24 -39 57 -145 96 128 26 -40 -56 -13 -102 23 -65 7 -70 29 26 13 -24 12 55 -12 43 -24 -47 56 18 -9 -23 -4 17 -10 34 -9 7 -20 -13 -18 10 12 -3 -8 5 -9 1 -3 16 2 -9 -3 -9 1 -8 -6 -1 8 2 -4 -9 7 2 -2 6 -3 -5 3 0 2 3 1 0 0 0
  -31 -59 -75 2 17 12 5 12 18 -34 -9 -10 15 25 25 25 -26 -19 39 -29 -34 6 8 40 33 10 -11 16 13 21 15 -7 -20 3 0 -12 0 -9 10 -1 3 1 4 -5 15 -6 9 -4 -2 7 6 1 4 2 1 2 1 0 -3 7 3 8 -3 -1 -2 1 6 0 1 4 7 6 1 -3 -1 -1 2 0 2 1 1 -5 2 -2 0 -1 -1 -1
  132 189 231 -41 -73 -53 -11 -1 -4 93 1 17 -111 -55 -91 -54 -8 74 -162 100 87 7 -30 -110 -50 -67 10 -44 4 -60 -4 24 36 -31 4 37 -18 22 -2 1 -4 4 -13 8 -17 20 -15 13 -16 -9 -10 -12 -13 6 3 -1 2 -1 3 -15 -8 -6 14 5 0 -8 -5 -7 -3 1 2 2 0 -1 1 2 -5 4 -4 -3 4 4 0 8 -1 -2 -3 -1
  -287 -328 -386 127 37 109 61 -105 4 -116 55 -57 250 100 147 70 86 -77 276 -132 -93 -58 68 139 102 119 -2 11 -45 81 -60 -19 -43 51 19 -40 35 -1 -7 -19 2 8 33 -9 26 -48 43 -5 31 -10 -3 23 11 -4 -5 1 -20 -15 -8 10 6 12 -15 -12 6 4 8 7 3 -3 -3 -3 3 -2 3 1 0 -1 -2 2 3 -5 0 -5 -1 3 -3 -1
  -155 -176 -185 60 144 73 -6 3 -48 -87 -44 -17 90 14 86 32 25 -100 160 -115 -94 -5 20 65 -6 84 -6 81 -11 40 -4 -39 -22 26 5 -58 33 -9 4 16 -8 -15 14 -10 -12 -19 2 -16 17 -7 3 2 12 -18 10 -7 -9 0 -1 4 -1 -7 -12 -6 3 5 0 14 -4 -6 -9 -2 6 3 -6 -1 7 -5 2 2 0 -2 -5 -3 4 -1 -3 0
  -75 -97 13 -45 128 51 33 77 -22 -34 -16 82 -4 17 22 6 -17 1 16 -43 -42 28 18 23 -14 3 -20 51 31 35 9 5 3 2 -52 -35 -25 -59 22 53 -61 -20 2 20 0 -2 -5 -34 -7 6 30 -1 21 0 -5 16 21 11 13 -12 7 -25 5 20 7 3 -6 7 7 6 2 9 0 4 -6 4 7 -7 3 0 -3 0 -3 1 6 6 3 -5
  349 437 327 -67 -115 -133 -132 45 7 145 -54 -35 -240 -101 -186 -39 -80 58 -267 147 133 46 -78 -140 -80 -135 25 -45 25 -113 64 9 33 -51 24 63 -15 59 -10 -38 60 11 -26 -19 -30 42 -38 33 -30 2 -21 -25 -24 5 18 -16 -7 7 -7 -2 -11 7 8 -7 -9 -11 -4 -5 -10 -2 -1 0 0 -5 1 -4 -8 4 3 -4 3 1 3 5 -3 -8 -4 0
  167 180 268 -89 8 -68 -22 89 -16 77 -22 71 -146 -61 -102 -46 -41 64 -175 68 62 40 -26 -79 -64 -80 4 -13 30 -38 33 22 35 -26 -34 27 -34 -18 4 25 -28 -7 -18 19 -16 29 -34 -13 -20 8 12 -11 0 5 -5 6 20 13 11 -13 3 -22 11 18 2 2 -13 -1 2 -1 -9 1 -5 6 -5 1 0 -6 2 -3 -6 5 -3 0 2 2 2 -2
  -237 -318 -347 -15 -90 38 160 -94 83 -147 98 -12 104 107 123 44 26 -14 178 -122 -112 -78 131 161 131 73 -27 -17 6 106 -18 4 -33 26 -14 -42 -30 -35 1 -7 -25 11 48 -26 30 -48 31 -11 13 7 4 -2 17 9 -8 22 -11 -10 -19 -7 6 0 -9 9 17 9 13 3 7 7 10 9 0 -5 5 13 13 -9 -2 11 0 -8 8 3 9 9 -3 0
  2 29 24 -59 -143 -41 29 -58 69 46 59 5 -1 27 -18 -31 42 60 -72 62 63 -26 16 -22 18 -36 -3 -82 -17 -16 -30 26 27 -15 9 29 -11 12 -8 -11 3 21 3 -4 11 -14 6 13 10 -5 -16 -8 -6 7 -3 11 4 -6 -9 -10 -5 4 -1 2 9 5 4 -11 6 -3 7 4 -12 -3 8 14 3 -3 -11 4 2 3 -3 1 -1 0 5 0
  157 202 177 -2 39 -11 -100 70 -36 77 -41 14 -59 -35 -93 11 -39 34 -110 63 82 63 -63 -58 -43 -70 10 -8 13 -43 22 17 11 -13 -21 33 -13 -1 0 -1 7 -1 -22 14 -5 24 -14 3 -14 6 9 3 -4 6 -1 1 15 12 13 2 3 -4 9 2 -9 -6 -8 -1 -1 3 -3 -2 -4 -1 1 -7 -5 3 2 -9 -2 4 -2 -3 -4 3 4 -2
  -190 -246 -162 23 100 68 93 -6 -41 -113 13 35 90 0 119 -14 30 -76 160 -92 -138 -25 27 65 5 95 -19 77 -11 61 -21 -31 -18 31 -11 -58 15 -37 17 39 -38 -19 0 15 -1 -11 10 -15 5 0 21 10 13 -6 -11 -6 2 3 12 9 -3 -13 -1 1 1 3 -2 6 -2 0 -5 -6 11 6 -6 -6 0 -4 4 1 3 -3 -1 2 -2 -3 1 -5
  198 253 227 19 80 -11 -148 92 -55 97 -69 11 -76 -50 -115 13 -50 19 -129 71 96 81 -87 -87 -67 -79 19 10 18 -66 26 10 16 -20 -7 28 -9 11 8 0 14 -8 -31 13 -15 31 -16 3 -18 5 10 2 -7 2 4 -6 11 11 13 1 2 -3 7 1 -10 -11 -8 1 0 4 -2 -1 -1 -1 -5 -8 -7 4 5 -8 -4 5 -3 -3 -4 -3 1 -2
  229 298 279 -60 -124 -111 -53 1 15 130 -15 -19 -164 -79 -118 -66 -23 70 -207 144 105 6 -59 -137 -72 -88 25 -48 -2 -90 23 10 36 -35 27 57 13 55 -18 -23 41 11 -20 -1 -21 35 -28 27 -16 -7 -26 -15 -24 1 12 -15 -6 2 -6 -3 -11 10 10 -9 -6 -9 -4 -9 -8 -6 0 -2 0 0 3 -2 -8 8 -2 -2 6 2 3 8 -3 -7 -1 1
  142 173 212 -26 -40 -46 -26 28 11 85 -8 18 -108 -30 -86 -27 -32 69 -143 84 83 17 -24 -92 -33 -65 16 -30 23 -51 8 24 24 -27 4 30 -23 18 -1 -2 2 -3 -9 3 -8 24 -6 5 -20 -5 -8 -8 -10 6 6 0 -1 -2 -1 -14 -3 0 9 9 0 -10 -1 -4 4 7 10 6 1 -1 -1 3 -4 7 0 -1 0 4 4 6 4 0 -3 -1
  51 76 117 -95 -29 -39 43 41 35 39 1 38 -114 -13 -31 -30 -43 49 -98 44 7 4 4 -34 -19 -44 -19 -2 30 -9 36 11 9 -26 -28 4 -21 -17 8 16 -19 -3 5 7 -6 12 -22 -10 -14 4 8 -15 5 7 3 5 8 6 3 -12 -1 -10 8 8 1 -3 -2 -1 -2 5 2 9 -1 1 3 3 1 -1 4 0 4 -1 3 3 3 1 0 1
  -29 -38 -233 34 -90 12 -24 -53 55 -75 32 -74 55 66 16 82 -19 -33 80 -59 -4 0 40 114 99 -5 -7 -32 14 37 18 5 -29 13 7 -6 -34 10 0 -49 41 21 22 -48 25 -31 28 21 -1 13 -4 -5 2 17 3 7 -11 -2 -21 3 -1 11 -12 -4 7 0 16 4 4 11 12 8 -8 -11 10 7 13 -8 0 4 -1 -3 5 -2 0 6 1 -3
  -204 -275 -310 34 41 73 57 -39 17 -127 39 -3 157 85 121 54 39 -59 198 -117 -99 -30 62 137 76 86 -12 25 -14 82 -26 -13 -33 38 -11 -43 10 -39 -3 6 -12 1 19 -7 27 -32 28 -13 23 7 8 14 16 -7 -8 11 1 -1 -1 13 9 7 -13 0 4 12 6 5 5 -2 3 -3 0 0 0 4 7 -3 -3 4 -3 -5 -3 -5 5 4 6 -1
  -51 -47 -71 49 37 52 -29 -16 -25 -13 12 -10 92 26 19 26 33 -17 66 -17 7 2 -5 20 9 17 5 4 -19 8 -28 3 -4 17 -4 -5 11 -1 -4 1 -1 0 -1 8 3 -9 14 0 8 -2 6 10 3 0 -1 2 0 0 3 0 1 0 -1 -2 0 -1 0 2 4 0 2 -2 1 -3 0 -1 -1 3 0 -2 3 0 -1 0 -1 2 2 0
  -193 -220 -183 -16 -61 38 107 -72 59 -51 66 15 96 81 77 4 50 24 90 -47 -42 -53 78 63 68 45 -18 -26 -7 59 -49 12 -4 14 -3 -21 -5 -16 -5 8 -30 6 31 -2 20 -35 25 -8 15 -7 -3 2 12 5 -3 18 -4 -7 -10 -15 -1 -1 -3 7 16 1 6 -4 5 2 10 7 -3 -4 5 13 7 -6 -9 6 3 -1 1 5 6 6 -1 -5
  441 544 639 -64 3 -122 -161 134 -57 243 -101 39 -284 -164 -237 -89 -90 117 -386 233 197 100 -157 -270 -166 -172 38 -25 28 -160 50 28 61 -64 8 87 -10 45 7 9 17 -9 -62 33 -36 77 -50 14 -44 -4 -7 -13 -30 5 9 -19 19 10 17 -6 -6 -2 25 3 -21 -20 -17 -11 -5 5 0 -1 -1 2 -6 -12 -15 13 2 -11 0 8 3 5 -8 -8 -1 2
  35 64 70 26 5 30 -41 7 6 58 4 7 27 31 -38 25 1 54 -44 49 75 24 -23 -38 7 -34 10 -31 2 -21 -25 28 7 -6 -3 24 -8 2 -2 -3 -3 1 -6 13 12 5 16 2 -3 -6 0 10 -3 7 -2 9 7 -1 4 -5 5 7 6 4 -2 -9 0 -5 7 9 12 6 -4 -4 4 0 -3 9 -5 -4 -1 3 3 1 0 3 2 -2
  -91 -127 -121 30 136 43 -17 41 -37 -58 -50 0 67 0 70 17 -2 -87 118 -79 -91 14 -11 53 -9 62 -13 76 -8 33 13 -39 -27 20 0 -39 39 -18 9 18 -3 -12 -3 8 0 -6 -5 -18 12 5 14 9 12 -14 1 -10 3 5 9 18 4 1 -10 -9 -8 6 -2 7 -5 -7 -11 -7 4 3 -6 -8 0 -4 5 -2 -1 -4 -5 -9 -2 -5 2 1
  -59 -70 -41 10 -27 -4 46 -39 11 -6 25 -9 37 10 31 -15 34 4 37 -3 -19 -35 19 4 14 29 7 -10 -19 9 -22 -5 -1 8 14 1 23 9 -10 -5 2 4 7 5 5 -4 6 -1 7 -8 -9 7 -1 -5 -1 -3 -7 -7 -3 2 1 7 -1 -4 1 2 0 0 0 -6 -2 -2 3 2 0 0 -4 3 -2 2 2 -3 0 2 0 -2 -2 0
  -327 -416 -376 140 152 166 46 -45 -36 -144 43 6 317 111 177 77 91 -92 310 -151 -113 -21 45 152 91 137 -7 44 -42 100 -83 -13 -41 66 -5 -55 26 -47 10 22 -36 -8 9 20 39 -44 57 -21 32 -2 23 39 19 -6 -21 10 6 -7 10 17 13 4 -13 1 3 9 3 5 14 1 3 -5 1 2 -4 -3 1 0 -4 0 -3 -2 -5 -8 -3 4 6 -3
  85 91 195 -50 -2 -44 15 36 -35 42 -13 49 -89 -78 -37 -75 -5 25 -101 58 9 9 -33 -78 -70 -20 3 5 -1 -30 0 2 27 -13 -9 15 -4 -9 1 25 -17 -8 -24 22 -18 26 -20 2 -12 -3 3 -2 -6 -4 -8 -6 13 8 14 2 -6 -13 11 5 -6 0 -11 -4 -4 -6 -9 -10 4 7 -4 -7 -8 1 1 -3 1 3 -4 4 -4 -3 3 -1
  63 47 -49 -36 -22 -43 -8 10 -7 -49 -5 -16 -73 -30 -8 5 -36 -44 3 -32 -44 -8 13 40 -8 -1 -4 20 10 3 50 -18 -9 -3 -7 -12 -10 -4 -3 -9 19 0 0 -22 -16 6 -22 6 -2 14 3 -15 -2 -3 4 -7 -7 7 -3 8 -1 -5 -5 -3 -1 8 -1 6 -8 -9 -9 -5 6 3 -2 -2 2 -5 8 2 -1 -4 -1 -1 1 -1 -1 4
  -27 -37 -83 -47 -126 -26 64 -54 54 -26 72 4 9 37 4 3 20 35 -4 -2 8 -34 52 48 53 -11 -12 -62 -1 23 -10 22 3 -1 -13 13 -30 -11 -10 -14 -4 18 12 -12 14 -15 6 9 5 7 -4 -6 1 11 -12 16 2 1 -5 -4 1 -2 1 7 10 8 4 -5 2 -2 0 2 -8 -1 9 8 4 -5 -7 1 -1 1 0 0 2 5 2 -1
  -12 -29 2 -36 -49 -27 55 -1 35 -9 24 17 -32 4 3 -15 -13 22 -18 -6 -13 -12 31 16 24 -6 -11 -16 16 20 7 9 1 -4 -9 0 -27 -9 5 1 -13 2 10 -4 6 -4 0 -4 -7 5 4 -5 4 9 -5 5 0 -1 -4 -9 -1 -8 1 8 6 0 1 -1 2 4 0 2 -3 1 3 5 4 -7 1 2 -2 2 2 0 2 3 0 -1
  -164 -238 -147 65 78 66 57 -14 -15 -67 18 14 142 44 100 10 46 -40 148 -73 -72 -28 33 56 37 90 -3 27 -17 51 -49 -8 -19 32 5 -29 18 -24 -1 17 -24 -12 5 16 17 -13 28 -16 15 -6 7 22 9 -9 -11 2 1 -7 7 7 7 2 -7 4 0 6 1 2 9 -1 1 -5 4 5 -4 -3 -2 4 -1 0 -3 1 -3 -3 2 1 1 1
  -52 -98 -26 -59 -44 -10 95 -5 28 -44 54 55 -22 18 7 -14 0 38 -7 -32 -30 -22 66 45 37 -1 -14 -25 21 44 -9 19 7 -1 -35 -7 -49 -43 5 18 -42 5 15 2 7 -10 2 -15 -6 7 12 -3 11 6 -14 23 10 3 -1 -11 6 -17 7 22 13 9 -1 1 4 3 -1 2 -1 2 -2 7 1 -9 -3 4 -3 0 -1 3 7 6 -1 -3
  -399 -508 -376 135 121 176 126 -63 13 -143 68 22 326 152 200 77 94 -40 308 -157 -105 -40 88 161 135 142 -16 18 -24 130 -100 7 -42 62 -13 -54 2 -58 15 26 -62 -5 33 21 57 -55 71 -35 31 -7 18 42 25 1 -24 26 7 -18 2 1 19 4 -10 12 10 7 10 3 23 15 13 6 -4 0 -1 7 6 0 -8 5 -8 2 0 -7 4 11 4 -2
  169 191 172 -8 14 -41 -83 59 -17 78 -45 4 -82 -42 -78 -10 -46 29 -108 69 55 39 -57 -77 -47 -48 23 3 12 -51 19 3 10 -14 13 27 10 16 -10 -8 23 -7 -22 9 -6 32 -11 7 -13 0 -4 4 -10 -2 4 -13 3 7 5 9 2 9 3 -3 -9 -9 -8 -3 -3 0 2 -3 3 1 -2 -9 -7 7 1 -5 -2 1 0 1 -1 -6 1 -1
  40 23 61 -66 -32 -21 25 23 16 -2 33 53 -57 14 -49 -2 -14 59 -70 0 35 7 42 4 6 -47 -3 -30 31 10 6 35 20 -9 -39 5 -55 -31 0 16 -37 0 9 -4 -1 -2 -7 -13 -9 10 9 -12 7 10 -5 21 11 7 -1 -20 6 -20 4 22 14 3 -3 0 6 5 3 6 -5 0 -2 13 9 -10 -3 0 -5 3 -1 3 10 9 0 -3
  -104 -116 -52 35 51 34 25 -18 -14 -13 6 7 82 17 46 3 45 -11 64 -29 -19 -11 8 15 10 38 1 2 -26 17 -29 -5 -4 13 2 -6 22 -6 4 13 -19 2 1 15 8 -12 5 -11 15 -7 -1 9 1 -7 -5 3 3 -4 5 3 4 1 1 -1 0 6 -2 0 1 -6 -7 -2 -3 4 -2 1 -2 0 -5 -1 0 0 -4 -5 -3 1 -1 0
  4 60 63 59 55 42 -74 -15 -57 54 -25 -10 70 -19 -20 -2 54 -1 -3 38 65 23 -57 -56 -46 -10 19 -3 -39 -38 -32 -2 17 6 13 19 40 26 -6 4 6 4 -17 18 -6 0 2 6 10 -12 -7 9 -5 -5 1 -6 4 -2 7 2 -3 4 4 -10 -5 -3 -4 -3 -1 -5 -4 -4 -5 -3 0 -4 -3 5 -6 -4 3 2 -2 0 -6 -1 3 -1
  -51 -101 54 -57 -58 -22 133 -17 31 -9 69 67 -12 1 29 -55 21 61 -22 17 -25 -39 41 -8 17 11 -8 -28 1 27 -27 20 15 -1 -20 5 -23 -31 5 28 -48 0 1 27 10 3 1 -16 -4 2 10 4 2 6 -20 12 11 -4 6 -9 5 -8 11 17 5 5 -3 -7 6 4 1 -1 0 5 -1 4 -3 0 -5 3 -1 2 3 3 4 0 2 2
  165 194 152 -5 6 -15 -120 64 14 90 -27 10 -41 21 -107 39 -37 63 -127 63 133 64 -37 -47 -7 -91 15 -46 28 -45 13 38 15 -18 -12 40 -32 4 -4 -12 10 4 -11 -2 11 12 2 0 -9 7 -1 -2 -3 9 3 12 13 5 1 -9 8 4 0 11 0 -4 0 -4 11 10 11 9 -14 -5 2 7 4 2 -5 -5 -7 7 -1 -6 5 6 4 0
  83 103 140 -37 -99 -58 22 -16 17 52 30 21 -75 -33 -52 -53 3 52 -107 66 50 -12 -1 -61 -21 -38 9 -45 7 -29 -11 21 30 -18 7 24 -26 14 -7 -7 1 3 -4 -2 -11 11 -4 13 -13 -5 -8 -6 -8 8 -3 0 -1 -1 -3 -12 -7 -7 5 7 6 -5 -2 -5 2 0 1 -3 0 2 1 3 -3 -2 0 1 -1 5 0 7 -1 -1 1 -2
  105 174 98 -44 -16 -23 -50 25 -8 38 -24 7 -105 -24 -67 0 -35 20 -99 43 51 26 -23 -43 -45 -57 0 -1 21 -39 35 10 16 -23 -13 7 -21 7 -2 -2 9 -6 -3 -17 -19 13 -17 12 -11 0 -4 -19 -3 5 12 -2 -1 7 1 -11 -9 -10 1 0 2 -7 -3 1 -5 -1 3 5 0 0 4 4 5 -2 3 -2 1 1 -1 4 1 4 2 -4
  -132 -177 -123 29 25 81 59 -21 2 -65 77 53 126 72 44 43 40 23 88 -44 -14 -3 45 79 73 15 -2 -25 -1 56 -51 27 -4 25 -36 -7 -45 -55 17 19 -50 4 0 19 32 -21 36 -14 -1 6 25 21 12 12 -28 26 17 0 10 -1 15 -9 6 21 8 3 -1 0 17 13 10 4 -5 -1 -2 5 -2 -2 -8 -1 -5 -1 1 1 1 7 5 -8
  -7 2 -55 64 37 13 -37 -20 -39 -23 -38 -48 18 -26 14 12 1 -59 56 -32 -27 -2 -16 3 -14 33 9 34 -13 -10 7 -28 -14 7 30 -13 28 29 -3 -15 27 -3 0 -15 -14 0 0 11 4 -5 -11 -1 -5 -9 10 -16 -17 -5 -4 9 -7 8 -6 -14 -5 -1 3 4 -9 -5 -6 -6 8 -2 -4 -7 -2 2 4 0 2 -3 0 0 -3 -5 -6 1
  369 458 392 -132 -201 -168 -65 29 52 162 -6 4 -301 -83 -203 -59 -84 132 -344 181 171 24 -44 -157 -69 -167 21 -93 39 -113 65 43 51 -69 4 77 -50 44 -14 -29 35 15 -15 -21 -25 43 -43 30 -31 4 -26 -38 -27 14 14 -1 -2 5 -11 -18 -9 1 14 7 1 -9 -3 -12 -6 0 7 8 -5 -2 5 8 -1 4 -1 0 0 4 5 8 3 -1 -2 4
  -222 -289 -131 14 140 76 86 10 -35 -78 -5 54 125 23 126 -20 52 -56 154 -81 -126 -24 23 45 -6 105 -18 75 -22 59 -42 -29 -13 30 -7 -51 43 -42 11 52 -50 -23 -2 34 5 -11 10 -30 20 -5 18 20 17 -17 -11 0 10 0 15 9 5 -7 -5 0 -1 8 -6 2 1 -8 -7 -7 7 8 -8 -5 -1 -2 -1 1 -2 -3 -6 -2 -1 -4 2 -3
  123 159 70 -38 -107 -70 -7 -4 48 31 14 -31 -120 -18 -51 -4 -54 25 -91 51 31 0 -6 -23 7 -53 5 -25 26 -29 45 9 2 -23 10 15 -30 23 3 -32 34 6 4 -27 -5 12 -9 19 -21 5 -7 -16 -11 13 9 -10 -12 -1 -11 -5 -6 5 -1 -3 -1 -12 4 1 -2 8 8 5 1 -1 5 3 1 0 7 2 2 -1 7 4 -1 -2 -1 1
  -63 -88 29 3 67 16 52 20 -30 -21 -17 26 12 -29 41 -32 14 -18 32 -26 -48 -4 2 -8 -23 40 -9 35 -5 18 -8 -11 0 8 -9 -17 9 -18 8 27 -29 -12 -3 18 -6 3 -7 -16 1 -5 7 5 6 -6 -6 -3 8 -1 10 0 0 -11 2 3 -4 4 -5 3 -1 0 -10 -5 2 5 -3 -4 1 -1 1 -1 -2 2 -2 -2 -1 0 0 2
  326 396 453 -55 -81 -122 -79 65 -23 171 -24 35 -211 -115 -177 -80 -47 103 -295 174 158 48 -87 -176 -96 -128 28 -64 16 -108 26 36 53 -47 -1 77 -36 29 -3 -8 13 3 -40 17 -24 54 -34 19 -32 0 -7 -10 -24 9 -4 -9 12 5 12 -10 -6 -9 18 8 -9 -9 -13 -10 -1 -1 -6 -7 -4 6 -1 -4 -12 6 2 -8 -4 10 -3 2 -6 -3 3 2
  226 281 228 -89 -144 -134 -35 8 36 101 -23 -27 -193 -77 -105 -61 -48 50 -200 111 74 4 -39 -101 -55 -81 8 -44 11 -74 52 4 26 -41 25 46 -2 46 -13 -30 43 10 -11 -18 -21 27 -36 25 -14 1 -24 -24 -19 3 12 -16 -6 1 -9 -2 -11 6 1 -10 -6 -4 -2 -8 -10 -6 -5 -2 -4 0 5 0 0 -1 2 0 1 1 2 2 -4 -6 -2 4
  -54 -80 -93 80 101 74 -39 4 -50 -43 2 2 110 30 29 46 28 -37 103 -51 -8 10 -2 36 7 34 13 28 -13 17 -27 0 -9 26 -8 -18 8 -13 -2 10 -9 -9 -4 9 3 -4 17 -9 9 1 11 15 5 -4 -4 2 0 0 7 4 8 -1 -4 2 0 1 -1 6 6 1 1 -3 5 1 -5 -2 0 5 1 -2 -4 1 -1 -3 4 1 3 1
  -32 -68 -76 0 70 50 -9 44 0 -38 24 42 51 61 5 58 -13 9 48 -44 -7 22 27 62 37 -8 0 11 23 35 0 19 -9 14 -40 -15 -30 -46 6 16 -28 -7 5 8 17 -5 13 -21 -3 13 25 10 15 6 -10 17 12 9 6 -2 16 -8 -1 16 7 1 -3 6 11 8 7 7 -1 1 -3 3 3 -2 2 -1 -6 -1 1 -2 8 6 4 -4
  -135 -136 27 10 190 63 17 55 -61 4 -68 47 53 -13 61 -27 32 -34 61 -40 -60 9 -17 -27 -64 63 -13 81 -15 16 -19 -27 0 9 -15 -37 55 -24 5 54 -44 -24 1 37 -16 2 -15 -36 17 -15 10 10 16 -24 7 -1 11 2 16 -3 2 -11 1 -2 -4 5 -10 6 -5 -10 -14 -3 5 7 -9 -5 -1 1 1 -1 1 0 -10 -3 2 -1 -1 1
  244 299 264 -91 -43 -69 -69 78 23 104 -11 40 -183 -25 -144 2 -80 100 -221 103 120 54 -35 -82 -38 -130 12 -43 44 -61 54 41 28 -43 -33 43 -52 -9 3 -1 -2 3 -12 0 -6 31 -27 -1 -25 11 5 -18 -7 13 4 9 14 11 3 -12 7 -6 11 14 0 -7 -7 -3 2 9 9 11 -5 -1 1 6 1 2 1 -4 -4 1 3 1 5 3 3 1
  

• PROPERTIES
  Unimodular=1
  

• REFERENCES
  I. Gauvin, Even unimodular ideal lattices of rank 88 over Q(zeta_115), preprint, 15 October 2026 (arXiv identifier pending),
  and its addendum: two further extremal lattices, X4969 and X4049 (October 2026).
  Data, programs and certificates: https://github.com/Katabolanga/rang88-reseaux-ideaux
  

• NOTES
  The two generators span a subgroup of the automorphism group, hence the catalogue sections SUBGROUP_ORDER, SUBGROUP_NAME and SUBGROUP_GENERATORS; the full automorphism group is not known.
  SUBGROUP_NAME: C115 : C4 = <zeta> : <g2>, zeta of order 115, g2 of order 4 with g2^2 = -1 and g2^-1 zeta g2 = zeta^24 (C4 acts through C2); equivalently C23 x Dic5.
  X4969 = (P, b), an ideal lattice over L = Q(zeta), zeta = zeta_115 (rank 88): P = (4969, zeta^2 + 3763*zeta + 2809) is a prime ideal
  of Z[zeta] of residue degree 2, and b(u, v) = Tr_{L/Q}(alpha u conj(v)), alpha = beta_0/nu totally positive (see the paper, section 6).
  Minimum 8 is established by the computer-assisted method of the paper (same certifying program, same execution model of section 5.4:
  M1, M2, H1-H3), as reported in the addendum: both sides of the criterion were swept completely, each side twice on two different
  machines, with byte-identical receipts and no hit. The attached Python scripts check the exported matrices and generators, not the minimum.
  The kissing number 168498000 follows from that minimum-8 statement and the extremal theta series.
  Basis: an LLL-reduced Z-basis of P; X4969_construction.gp gives it in the power basis of Z[zeta], together with alpha.
  Generators (row convention, g*GRAM*g^T = GRAM): g1 = multiplication by -zeta, of order 230;
  g2 = the semilinear map u -> lambda*sigma_24(u), sigma_24(zeta) = zeta^24, lambda a unit of Z[zeta] (in X4969_construction.gp);
  g2^2 = -1, and g2 o g1 o g2^(-1) = g1^139 as maps (in matrices: g2^(-1)*g1*g2 = g1^139).
  <g1, g2> has order 460 = 2^2*5*23: an extension of the Galois stabiliser <sigma_24> (order 2) of the class of P by the cyclic group
  <-zeta> (order 230). By the normaliser argument of the paper (Remark 2.6) and the stabiliser of the class (support {3,331}, see the
  addendum), it is the normaliser in Aut of the group of multiplications by roots of unity. The full automorphism group has not been
  determined: |Aut| >= 460.
  A vector of norm 8 (transported to this basis), as a row of coordinates in this basis:
  NORM8: 100 151 118 -34 -57 -37 -21 3 12 53 -4 0 -87 -24 -65 -9 -25 50 -106 59 61 16 -19 -48 -19 -60 7 -29 11 -32 20 14 15 -20 -5 25 -18 12 -1 -10 7 7 -2 -6 -4 10 -11 10 -11 0 -8 -10 -7 7 5 1 0 1 -2 -7 -3 0 8 0 -1 -6 -1 -3 -2 5 4 5 -3 -3 3 4 1 0 -2 0 1 0 2 4 0 2 0 -2
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe