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 Fri Jul 18 13:18:13 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  L_56,2(tilde(M))
  

• DIMENSION
  56
  

• GRAM
  56 0
  8
  -2 8
  -1 -3 8
  0 -2 3 8
  -1 -2 0 3 8
  -4 -1 1 2 4 10
  -1 -2 2 3 2 2 8
  -3 4 -3 1 -2 0 -3 12
  0 2 0 -3 -4 1 -3 0 10
  -1 3 0 2 -2 -2 -1 1 0 10
  2 -1 2 -2 -2 -2 0 -5 4 -2 10
  1 -2 -2 -2 2 -2 0 -1 -2 0 -3 10
  -3 1 3 1 -3 3 -1 5 2 1 -3 -1 12
  -3 -3 3 2 4 3 -1 0 0 -1 1 2 -1 12
  3 0 1 -1 1 0 2 -4 -2 1 2 2 0 0 12
  -3 1 3 4 4 4 1 3 -2 2 -4 1 4 4 0 12
  1 -1 -3 -2 0 -3 2 0 0 -4 3 1 -2 -3 0 -3 12
  -3 2 2 3 0 1 2 4 0 -1 0 -5 1 0 -4 3 2 10
  -2 1 -2 2 4 3 3 0 -1 0 0 1 -3 4 2 3 2 0 10
  -4 3 2 1 -2 1 2 1 -1 2 1 -4 4 0 1 1 -2 2 0 10
  -4 0 -1 -2 0 4 2 -2 3 0 2 -2 -2 2 -1 -2 1 1 2 1 10
  1 1 1 -2 1 -3 2 -2 -1 -3 4 -1 -4 -1 2 -2 3 2 0 -1 -1 10
  -1 -1 3 2 -1 1 0 0 3 2 0 1 4 3 -1 4 -2 1 -1 1 1 -3 8
  -2 2 -3 -4 1 -2 1 0 1 -4 4 -1 -5 -2 -3 -3 6 2 2 0 3 6 -3 14
  1 -3 0 0 -2 -3 2 0 1 -1 0 3 0 -2 -1 -4 4 -2 -1 -3 0 1 1 2 10
  -3 -1 -1 0 1 3 -2 1 1 3 -1 2 2 2 0 1 -2 -4 2 -1 1 -4 1 -1 1 10
  0 3 1 1 -2 1 -1 3 3 -1 0 -2 4 -1 -1 2 -2 3 -1 1 -2 0 3 -1 0 -2 8
  2 3 1 -1 -4 -4 -3 0 0 4 0 -2 2 -3 1 1 -4 -1 -4 2 -3 -1 1 -4 -3 -1 2 10
  0 0 2 2 2 -2 -2 1 -1 -1 0 1 1 2 -2 3 0 1 0 -1 -5 2 1 1 0 0 2 0 8
  2 -2 -1 3 3 2 0 -2 0 0 0 1 -3 2 -1 0 -1 -2 3 -2 -1 -3 0 -1 0 2 -1 -3 0 8
  0 -2 1 0 -2 0 -1 -1 3 1 1 -1 1 0 -3 -1 -1 -2 -2 0 2 -3 2 0 2 2 -1 1 -1 1 6
  -3 4 -3 -1 -1 3 -3 5 5 2 -1 0 1 3 -4 1 -3 1 2 -1 4 -2 2 0 -1 2 3 -1 -2 1 0 12
  -1 4 -2 -4 -1 -3 -4 4 -1 2 0 -1 1 -2 1 2 0 1 -3 2 -2 3 -1 5 -3 0 0 4 1 -4 -1 -1 14
  3 -2 -3 0 0 -3 2 -1 -2 -3 -1 3 -3 -1 -2 -3 4 0 0 -1 -1 0 0 1 2 -4 -1 -2 0 2 0 -2 -3 10
  0 3 1 1 -3 0 2 0 3 3 -1 0 3 -3 -1 2 -2 2 -1 1 0 -1 4 -3 1 -2 5 3 -1 -1 0 3 -2 0 10
  -2 1 3 1 -3 -3 -2 2 1 1 3 -4 2 2 -3 0 0 2 -2 4 0 0 2 0 0 0 1 4 2 -2 2 0 1 -2 0 10
  -3 1 -1 1 4 2 2 1 -1 -3 0 -2 -1 -1 -3 1 3 4 1 0 1 4 -1 6 0 0 1 -2 2 -1 -1 0 2 0 -1 0 10
  4 -4 4 4 3 -3 1 -6 -3 -1 1 1 -5 3 1 1 -1 -1 1 -2 -4 1 1 -2 1 -3 -1 1 4 3 0 -6 -4 2 -1 1 -1 14
  -2 -2 1 1 4 2 0 -3 0 -2 -1 1 -1 1 -4 1 1 -1 0 -1 1 -1 1 3 2 2 -1 -3 3 2 2 -1 -2 0 -1 1 3 3 10
  1 -3 1 -2 -2 2 -1 0 0 -2 1 1 3 -1 2 0 -1 -3 -3 -1 -1 -2 0 -2 1 3 0 0 -1 0 1 -2 1 -2 -1 -1 -3 -2 -2 10
  -1 3 -1 -2 0 0 1 1 -1 0 -3 0 -1 -1 1 0 -2 1 1 0 0 3 -3 1 -1 -2 0 0 -1 -2 -3 1 1 0 1 -3 0 -1 -2 -2 8
  -2 -3 2 4 1 -1 1 1 -1 2 -2 3 2 5 -1 1 -1 -2 2 1 -1 -3 4 -2 5 4 0 -1 3 1 2 -1 -3 1 0 3 0 4 3 -2 -2 12
  -2 4 -2 2 1 2 3 1 1 4 1 -4 0 -4 2 0 1 3 2 4 2 1 -1 3 -2 2 0 -1 -2 0 -1 0 3 -2 1 -1 5 -5 -1 -3 0 -1 14
  3 -1 -3 2 -1 -1 2 0 0 0 2 0 -1 -3 2 -3 5 0 3 -1 0 -1 0 0 3 1 0 -2 -1 2 0 -1 -3 3 0 -2 0 0 -2 0 -3 1 3 10
  -4 0 0 2 -1 2 2 2 0 2 -2 -1 3 -1 -3 -1 -1 0 0 4 2 -3 1 0 3 3 0 -2 -1 0 2 1 -2 -1 1 1 1 -3 2 0 -1 4 3 1 8
  -2 -2 4 3 0 1 -1 0 -2 3 -1 -3 1 2 -2 2 -3 3 -3 2 0 -2 2 -3 -2 0 -1 1 1 0 1 -2 2 -2 -1 2 -1 3 1 1 -2 1 -1 -2 1 10
  -4 0 1 2 2 4 -1 1 -1 -1 -2 -4 1 2 -3 1 -3 3 0 2 2 -2 1 0 -2 2 1 0 1 0 0 0 1 -2 -2 2 3 1 3 -1 0 2 1 -1 2 4 10
  -1 0 1 -3 1 -2 -1 -1 -2 0 2 3 -2 4 5 0 -1 -3 0 0 0 4 -1 1 0 1 -2 1 1 -3 -2 -1 4 -3 -3 1 0 1 -2 2 1 1 -2 -3 -2 0 -1 10
  1 -2 0 1 2 2 -2 1 -1 1 -2 1 -1 2 2 1 -2 -2 1 -3 -1 -2 -1 -2 -1 3 -2 -2 0 2 0 0 0 -2 -4 -3 -2 1 0 2 -1 0 -1 0 -1 3 0 1 8
  2 -1 -3 1 1 1 -3 0 -1 2 -2 1 -2 1 0 -2 -2 -3 0 -2 0 -4 -1 -4 -1 2 -2 -1 -1 4 0 2 -2 1 -2 -2 -3 1 0 1 -1 0 -1 2 0 2 1 -1 3 8
  2 3 -2 -1 -1 -3 -4 4 2 0 0 -1 0 -1 0 1 1 0 0 -2 -3 1 0 2 0 0 2 3 2 -1 0 1 4 -1 -1 2 1 1 -1 -1 0 0 0 0 -3 -2 0 1 1 -1 8
  3 2 0 -1 1 1 2 -3 1 -1 1 -2 -1 -4 5 1 0 0 1 0 -1 3 -1 2 -2 -2 1 1 -1 0 -2 -3 2 -1 1 -3 1 1 -1 0 3 -4 4 0 -3 -3 -1 -1 0 -2 2 10
  -4 4 1 1 1 3 -1 2 1 1 -1 -5 1 -1 -4 4 -2 5 1 2 0 1 0 2 -4 0 3 1 2 -1 -1 2 3 -4 2 1 4 -1 2 -2 1 -3 3 -3 1 3 4 -2 0 -2 1 1 10
  -1 -2 0 3 0 1 0 0 1 4 -1 2 0 4 -3 0 -4 -1 1 0 2 -5 4 -3 1 3 0 -1 -1 4 2 4 -3 1 2 0 -2 0 0 -1 -2 5 0 1 3 2 1 -2 0 3 -3 -4 -2 10
  1 -3 3 3 2 -2 1 1 -4 1 0 1 -1 4 1 3 -1 0 1 -1 -3 3 0 0 1 -1 -1 -1 3 0 -1 -2 2 -1 -2 1 -1 3 -1 0 0 3 -2 -2 -1 2 -2 3 2 -1 0 -1 -1 1 10
  1 -3 4 0 -1 1 2 -1 2 -3 4 -3 3 1 1 0 0 0 -2 1 1 3 1 2 1 -2 1 0 0 -2 2 -1 1 -1 -1 2 1 -2 -1 2 -1 0 0 -2 -1 -1 -2 1 -1 -4 0 2 -2 -1 4 12
  

• DIVISORS
  1
  

• MINIMAL_NORM
  6
  

• KISSING_NUMBER
  15590400
  

• HERMITE_NUMBER
  6
  

• SUBGROUP_ORDER
  2^3*3*7*29
  

• SUBGROUP_NAME
  plm C29 . C14 circ tilde(S)_3
  

• SUBGROUP_GENERATORS
  4
  56 56
  1 3 1 4 -5 0 7 -3 2 0 -1 3 2 3 -1 -2 0 0 -1 -2 2 -1 -1 0 -3 1 2 0 -1 1 -1 -2 3 0 -2 1 2 -1 2 0 1 -1 -2 1 1 -1 -1 0 0 3 3 -1 1 -1 2 -1
  -15 -5 -6 17 2 -5 -10 -1 4 -9 -3 5 -3 -2 2 -1 8 -4 -4 6 1 7 3 1 -1 -4 -2 10 0 1 4 2 -4 -3 1 -3 -6 -1 0 5 6 0 4 2 -4 -1 1 0 4 -1 -2 2 4 4 1 1
  9 -3 5 -17 9 3 4 8 -2 9 6 -1 1 -4 -1 -2 -6 4 5 -1 0 -4 0 -2 1 0 1 -4 1 0 -1 -1 0 2 0 2 2 1 0 -2 -2 1 -2 -1 2 1 0 0 -3 0 1 -1 -1 -3 -1 0
  3 1 3 -1 0 1 2 3 0 3 2 1 2 1 -1 -1 -1 -1 1 -3 1 -1 -1 1 -2 1 2 -1 -2 0 -1 -2 1 2 0 1 1 1 1 -1 0 -1 -1 0 2 0 0 1 -1 1 0 0 0 -1 0 0
  17 12 3 -18 -5 13 9 2 -11 10 5 -3 3 8 -3 -3 -3 5 2 -7 -7 -7 2 1 4 0 -2 -5 1 -2 1 -1 0 0 -2 1 4 2 1 -3 -4 0 0 -3 2 0 1 0 -2 -1 -1 -1 -2 -2 -1 0
  -15 -18 3 15 13 -18 -16 5 14 -8 -5 2 -3 -12 1 6 1 -9 2 10 10 8 -4 1 -3 1 5 5 -4 2 -4 -1 -3 3 5 -1 -4 -2 -2 2 3 -2 1 3 -2 2 1 2 2 0 -2 2 0 1 0 0
  1 -3 5 2 3 0 -4 1 4 2 -1 1 -1 -4 0 -1 -3 1 5 0 1 -1 0 1 -1 1 1 -1 -2 -1 -3 -2 2 3 1 2 2 -1 0 0 0 -1 -2 0 2 0 -1 1 -1 1 0 -1 -2 -2 0 0
  -13 -5 -3 28 -8 -2 -16 -3 5 -10 -6 7 -3 1 1 2 9 -8 -4 6 5 9 -1 4 -1 -2 -1 10 -2 1 0 -1 -2 -1 2 -3 -4 -2 0 3 5 -2 3 2 -3 -1 0 1 3 -1 -2 3 3 4 0 0
  -18 -10 -9 8 9 -13 -5 -1 7 -9 -2 -1 -2 -8 4 3 2 -2 -3 5 1 5 1 -2 -2 -2 1 4 0 1 3 3 -3 -2 1 -1 -6 0 -1 3 3 1 2 2 -3 0 0 0 3 0 -1 1 2 3 1 1
  -13 -2 -8 17 -3 -3 -8 -4 3 -8 -2 4 0 0 3 1 5 -3 -5 0 0 5 1 3 -2 -3 -2 7 -2 1 2 2 -3 -1 0 -1 -5 0 0 3 4 1 3 2 -1 0 0 1 2 -1 -2 2 4 2 1 1
  0 -2 4 -9 8 -3 6 3 1 1 3 -2 -2 -6 -1 -1 -3 1 2 1 1 -3 1 -5 -1 1 2 -4 2 0 0 0 3 0 0 1 1 0 -1 -1 0 1 -2 0 0 -1 -1 -1 0 2 2 -2 -1 -1 0 0
  6 11 -8 -5 -11 6 8 -6 -8 2 0 -5 5 12 1 0 0 3 -3 -8 -9 -3 1 3 3 -2 -4 -1 0 -2 3 3 -2 -2 -3 -1 1 1 2 0 -4 1 2 -2 0 1 1 0 -1 -2 -2 1 0 0 0 -1
  -29 -30 3 43 9 -25 -32 4 25 -17 -13 9 -7 -16 4 8 7 -17 0 18 19 17 -7 4 -7 0 5 14 -6 4 -7 -1 -4 4 7 -4 -7 -5 -1 6 7 -3 2 6 -5 2 0 3 2 -1 -2 4 3 3 1 -1
  3 -1 -1 -15 8 -4 4 5 -2 4 4 -6 3 -2 0 2 -5 2 2 -2 -2 -1 -1 -2 1 0 1 -4 -1 0 1 1 -2 1 0 0 0 2 0 -1 -4 2 0 -1 0 1 1 0 -1 -1 -2 0 -1 -1 -1 0
  -18 -14 4 31 5 -14 -20 0 16 -12 -8 10 -5 -9 0 1 5 -9 2 12 11 9 -2 2 -4 0 2 11 -5 2 -4 -2 -2 2 4 -3 -3 -5 0 5 6 -3 1 4 -3 1 0 2 2 1 0 2 2 0 3 0
  -4 -6 0 10 2 1 -9 5 2 0 0 6 2 1 -1 -2 4 -4 0 2 2 5 1 5 0 -5 0 10 -3 1 1 -1 -5 1 0 -1 -4 -1 2 3 4 -1 4 2 -2 0 1 3 1 -1 -3 3 4 1 0 -1
  9 3 10 6 -10 14 -9 -2 -3 1 -6 3 -7 1 -2 -3 3 1 4 4 1 -1 2 2 3 2 -3 1 3 -2 -3 -2 3 0 1 -1 3 -2 -1 -1 -1 -2 0 -2 0 -2 -2 0 -2 -1 1 -2 -3 0 -1 0
  13 10 6 -17 -2 16 8 6 -12 10 7 -1 -1 5 -3 -7 1 5 2 -5 -6 -6 5 -2 3 -1 -2 -2 4 -2 3 -1 2 -1 -2 0 2 3 1 -2 -1 0 0 -3 2 -3 0 -1 -1 0 0 -1 -1 0 -2 1
  -2 -2 1 7 -1 -3 -6 0 1 -3 -4 0 -1 1 -1 1 3 -4 0 3 1 3 0 2 0 0 0 2 -1 0 0 0 -2 -1 2 -2 -1 -1 -1 1 0 -1 2 0 -2 0 1 1 1 -1 -2 1 0 1 -1 0
  -23 -20 0 24 12 -18 -18 3 17 -11 -4 5 -4 -15 3 4 1 -8 1 10 11 10 -2 0 -5 -1 3 8 -4 3 -4 -1 -1 3 4 -1 -5 -3 -1 4 6 0 0 4 -3 0 -1 1 3 1 -1 1 2 1 1 0
  -6 -10 3 -5 18 -13 -6 4 9 -3 -2 -4 -3 -13 2 4 -4 0 4 6 4 2 -2 -3 -1 3 3 -2 -1 0 -2 1 -1 3 3 1 -2 0 -3 1 -1 1 -1 1 0 2 0 0 0 0 -1 -1 -2 0 0 1
  19 16 5 -22 -7 22 11 0 -15 12 7 -1 -1 6 -3 -8 -3 11 4 -7 -10 -10 6 -3 5 -1 -5 -7 5 -3 3 -1 4 -2 -3 2 6 2 1 -3 -3 1 -2 -4 3 -3 -1 -2 -2 0 2 -3 -3 -2 -1 1
  -12 -8 -5 0 12 -14 2 4 6 -3 1 -4 3 -4 2 2 0 -4 -2 0 1 3 -1 -1 -3 -2 3 3 -2 1 2 3 -3 1 0 -1 -5 1 1 3 1 1 2 2 -2 1 1 1 1 0 -2 2 2 1 1 -1
  32 29 -1 -42 -10 31 25 -3 -27 18 11 -10 2 15 -4 -8 -5 16 1 -14 -21 -18 9 -3 11 -1 -8 -14 9 -6 7 2 3 -5 -6 3 7 4 -1 -6 -7 3 -1 -7 2 -2 0 -3 -3 -2 0 -4 -4 -2 -3 1
  5 8 -4 -8 -4 7 5 -6 -6 2 1 -4 0 3 1 -1 -3 6 1 -5 -8 -6 2 -1 3 1 -3 -6 2 -3 2 2 2 -1 -1 2 2 1 -1 -2 -3 0 -1 -2 2 1 -1 -1 -2 -1 1 -1 -3 -1 0 1
  -12 -5 -5 20 -4 -9 -12 -6 5 -11 -6 1 -2 0 1 7 5 -9 -5 5 3 5 -3 3 0 0 0 3 -2 0 -1 2 -3 -1 3 -2 -3 -2 -3 1 2 -1 3 2 -3 2 1 1 2 -2 -2 3 1 2 0 0
  -7 -3 -4 -5 9 -9 7 5 0 -1 3 -3 2 0 0 -1 3 -3 -3 0 -1 1 1 -3 -2 -2 2 2 1 1 5 3 -2 -2 0 -2 -4 2 1 2 2 0 2 1 -2 0 2 0 2 0 -1 2 2 2 0 0
  -16 -15 2 20 7 -14 -10 4 13 -8 -3 8 -1 -8 1 1 4 -8 -1 8 12 9 -3 0 -6 -1 4 9 -3 4 -2 -1 -1 2 2 -2 -4 -2 1 4 6 -1 1 4 -2 0 0 1 2 2 1 2 4 1 2 -1
  30 26 -2 -36 -12 25 24 1 -25 18 10 -8 7 20 -4 -7 -2 11 -2 -15 -17 -13 5 0 7 -2 -6 -9 5 -4 7 2 -1 -4 -6 0 5 5 3 -4 -7 2 1 -5 2 -1 2 -1 -4 -3 -1 -1 -1 -1 -2 0
  -3 0 -4 5 -3 -2 0 -5 0 -4 -2 0 0 1 0 2 1 -2 -2 0 -1 0 0 1 0 0 1 -1 0 0 1 1 0 -2 0 1 -1 -1 -2 -1 1 0 1 0 -1 1 0 0 1 0 0 0 0 0 0 0
  -10 -12 2 13 7 -8 -16 -1 11 -7 -5 4 -4 -13 2 4 -2 -1 4 8 8 6 -2 0 -2 2 2 2 -3 1 -4 -2 0 3 3 1 -2 -2 -2 1 2 0 -1 2 0 1 -2 1 0 1 1 -1 -1 0 1 1
  -22 -16 -7 14 12 -22 -8 1 13 -12 -5 -1 -1 -10 5 7 3 -8 -4 7 7 10 -4 -1 -5 -1 4 5 -2 3 1 3 -3 0 3 -1 -7 0 -2 4 3 1 2 3 -3 1 1 0 4 0 -2 2 3 4 0 0
  3 14 -3 5 -15 19 2 -3 -13 1 6 6 0 11 -4 -7 7 1 -4 -5 -7 -3 7 1 5 -6 -6 6 3 -1 5 0 0 -4 -4 -2 -1 0 2 0 4 0 4 -1 -2 -3 0 0 2 -1 -1 2 3 1 0 0
  6 7 2 0 -7 7 1 -7 -1 2 -4 -1 0 2 0 -2 -2 6 3 -3 -3 -2 1 1 0 2 -1 -3 -1 -2 -1 -1 4 1 -2 2 3 0 1 0 -2 0 -2 -1 2 -2 -2 0 -1 1 1 -3 -3 -1 1 0
  -22 -14 -3 21 9 -17 -10 3 12 -10 -5 3 -2 -6 3 1 7 -10 -3 6 6 9 0 1 -6 -3 3 10 -3 2 1 2 -3 0 2 -3 -7 -1 1 6 6 -1 3 4 -3 0 1 1 3 0 -2 3 4 3 1 0
  -6 -14 5 8 10 -8 -10 5 9 -4 -2 4 -3 -10 0 2 0 -5 2 9 10 5 -3 -1 -2 1 3 3 0 2 -3 -1 0 2 3 0 -2 -2 -2 1 3 0 0 2 -2 1 -1 0 0 0 1 0 1 0 0 -1
  16 13 5 -18 -8 17 7 1 -13 10 5 -4 -1 6 -2 -3 -2 6 2 -7 -8 -8 3 -1 4 1 -3 -8 3 -3 1 -1 3 0 -1 1 5 3 0 -4 -4 0 -1 -4 3 -2 0 -1 -2 -1 0 -2 -4 -1 -2 1
  34 27 -1 -52 -5 23 37 3 -25 24 15 -12 10 18 -4 -9 -10 16 1 -20 -19 -19 5 -3 6 1 -3 -16 5 -4 6 1 2 -2 -7 3 8 6 3 -7 -10 2 -3 -6 5 0 1 -2 -6 0 2 -3 -3 -5 -1 0
  22 12 -1 -30 -1 14 15 2 -14 13 7 -7 5 8 -2 -2 -6 9 1 -8 -9 -9 2 0 6 0 -3 -8 4 -2 2 1 -1 -1 -3 2 3 3 0 -4 -6 2 0 -4 2 1 1 -1 -3 -2 0 -2 -2 -2 -2 0
  -9 -6 -1 13 3 -7 -6 -2 6 -6 -2 3 -1 -2 -1 2 2 -6 -1 4 3 2 -1 1 0 -1 2 4 -2 0 -1 0 -1 0 1 0 -2 -3 -1 1 4 -2 1 3 -2 2 0 1 1 0 0 2 1 0 1 -1
  6 9 -4 -7 -4 9 3 -5 -6 4 1 0 0 4 1 -3 -1 8 0 -3 -8 -4 3 0 3 -1 -4 -3 1 -2 3 1 0 -2 -2 2 2 1 0 0 -1 1 -1 -1 1 -1 0 -1 0 -1 0 -1 0 0 0 2
  3 6 -6 -8 -1 -2 7 -2 -4 2 2 -7 4 5 1 2 -3 1 -2 -6 -6 -4 -1 0 1 1 -1 -6 -1 -2 2 3 -1 0 -1 0 1 2 0 -1 -4 1 0 -1 0 2 1 0 -2 -2 -2 1 -1 -1 0 0
  -10 8 -7 18 -11 3 -1 -8 -2 -7 0 3 -1 6 0 -1 7 -4 -7 -4 -5 -1 3 2 -1 -2 -2 3 -1 -2 3 1 1 -2 -1 0 -2 0 0 1 5 -1 2 1 -1 -2 0 1 4 0 -2 2 2 2 1 1
  -10 -2 4 17 -4 -12 -1 -2 8 -8 -6 -1 -1 0 0 3 4 -9 -2 1 6 4 -4 0 -6 4 4 1 -3 0 -3 -1 3 2 2 -3 0 -1 1 1 0 -3 -1 1 0 -1 0 1 1 3 1 1 -1 2 1 -1
  -12 -2 -8 2 4 -9 1 -2 2 -5 3 -4 1 -3 3 4 -2 -2 -3 -3 -2 0 0 -2 -1 -1 0 -2 -1 0 1 2 0 0 1 1 -2 1 -1 0 1 1 0 1 0 1 0 -1 2 0 -1 1 0 1 0 1
  18 13 2 -27 -2 17 13 6 -16 13 11 -4 3 7 -3 -5 -3 8 1 -9 -8 -8 4 -2 5 -1 -3 -5 4 -1 3 0 0 -1 -3 0 2 4 1 -4 -4 2 0 -4 3 -1 1 -1 -3 -1 0 -1 -1 -2 -2 1
  12 12 0 -26 3 3 19 4 -12 8 10 -8 5 7 -4 -2 -3 3 -1 -8 -7 -9 1 -5 3 2 1 -9 3 -2 4 2 1 -1 -2 0 2 4 0 -4 -4 0 0 -3 1 1 2 -1 -1 0 0 1 -2 -1 -1 0
  5 6 -3 -6 -3 5 2 -1 -6 3 3 -1 2 5 -1 -1 -1 3 0 -3 -5 -2 1 0 3 -2 -3 -1 0 -1 2 1 -2 -1 -1 -1 1 0 1 0 -2 1 1 -1 0 1 1 0 -1 -2 -1 1 0 -1 0 0
  12 9 0 -5 -10 12 2 -1 -9 5 2 1 2 9 -3 -1 1 2 -1 -3 -3 -2 1 3 4 -1 -3 0 1 0 0 -2 -2 -2 -1 -1 2 0 0 -2 -2 0 1 -2 1 0 1 0 -1 -1 0 0 0 -1 -1 0
  -7 -3 -3 8 -1 -9 -2 -4 6 -6 -5 -2 0 -2 3 5 0 -3 -3 1 3 3 -4 1 -3 3 2 -1 -2 1 -2 1 0 1 1 0 -1 0 -1 0 -1 0 -1 1 0 1 0 0 0 0 0 0 0 1 1 0
  1 7 -4 3 -6 7 3 -3 -5 0 1 3 1 7 -2 -4 4 1 -3 -1 -4 -1 3 1 2 -2 -2 3 1 -1 4 0 -1 -3 -2 -1 -1 0 1 1 2 -1 2 0 -2 -1 0 0 1 0 0 1 2 1 1 0
  -4 0 0 12 -2 4 -4 -3 2 -2 -1 8 -2 1 -2 -5 3 -1 0 3 0 -1 4 2 1 -3 -1 6 0 0 0 -2 0 -2 -1 1 0 -3 0 2 6 -2 1 2 -2 -1 -1 0 2 1 1 0 2 -1 2 0
  9 8 -1 -17 -3 13 8 5 -15 8 8 -2 1 8 -3 -4 3 2 -3 -5 -7 -4 5 -1 4 -4 -3 -1 5 0 5 1 -2 -4 -1 -1 -1 3 0 -2 0 1 3 -2 0 -2 2 -1 1 -2 -1 1 1 1 -3 1
  -2 5 -10 -15 2 -7 16 -1 -4 1 5 -11 6 4 3 4 -4 1 -5 -10 -7 -4 -1 -2 -1 0 1 -7 0 0 3 4 0 -1 -2 1 -1 4 0 -2 -4 3 0 -1 1 1 1 -1 0 0 -2 0 0 0 -1 0
  19 13 3 -15 -10 16 12 1 -13 11 6 -1 4 11 -4 -4 -2 3 0 -9 -6 -8 1 1 3 -1 -2 -6 2 -1 1 -1 2 -1 -3 2 5 1 1 -4 -3 1 -1 -2 2 0 0 0 -3 -1 0 0 0 -3 -2 -1
  0 -15 7 7 8 -6 -11 3 13 1 -4 5 -2 -13 1 3 -6 0 7 7 10 3 -5 1 -3 2 4 -1 -3 2 -7 -4 2 5 2 4 2 -3 -1 0 1 0 -4 2 1 1 -2 2 -2 1 1 -2 -1 -3 0 -1
  56 56
  6 7 0 -3 -2 1 10 0 -5 1 3 1 3 8 -4 -2 4 -4 -4 -2 -1 -4 -1 -1 1 0 1 -1 2 -1 3 2 0 -2 -1 0 1 0 -1 -1 1 -1 1 0 -1 2 2 0 1 0 0 3 2 0 0 -1
  -2 0 2 6 -1 2 -4 -3 1 -3 -4 2 -3 -1 -1 -2 3 -1 0 3 1 1 2 0 0 0 0 2 1 0 0 0 1 -1 0 0 -1 -1 -1 1 2 -1 1 1 -1 -1 -1 0 1 -1 1 -1 0 1 1 0
  -1 -4 0 6 -1 11 -16 -2 0 0 1 8 -4 -7 0 -2 -3 7 6 4 1 2 4 1 4 -3 -4 4 0 1 -2 -4 0 0 1 2 0 -2 -1 0 3 1 0 0 1 -1 -3 0 0 0 1 -2 -1 -2 0 2
  -4 -7 6 16 -3 5 -16 -2 5 -3 -3 8 -5 -8 -1 -1 0 0 6 6 6 3 0 1 0 0 0 3 -1 0 -4 -4 3 2 2 1 1 -3 -1 0 3 -1 -1 0 0 -1 -3 1 0 1 2 -1 -2 -1 0 0
  5 8 -2 -13 1 -3 16 1 -6 3 6 -8 6 6 -2 1 -2 -1 -2 -8 -5 -5 -1 -2 0 1 2 -6 0 -2 3 2 1 0 -2 0 1 2 1 -2 -3 1 0 -2 0 1 1 0 0 1 -1 1 -1 0 -1 -2
  -12 -12 2 9 9 -14 -8 1 11 -6 -3 -2 -3 -11 3 5 -3 -4 3 5 5 4 -3 -1 -3 2 3 -1 -3 0 -3 0 1 3 3 0 -1 -2 -1 1 0 0 -2 1 -1 1 -1 0 0 1 0 0 -2 0 0 -1
  -9 -9 0 15 2 -5 -16 -2 8 -6 -5 3 -4 -8 2 4 0 -2 2 6 4 5 -2 2 -1 1 0 2 -3 0 -3 -1 -1 2 3 0 -2 -2 -2 1 1 0 0 1 -1 1 -1 1 0 -1 -1 0 -1 0 0 1
  5 -2 2 -1 -3 5 0 -2 2 3 -4 0 -1 -1 1 -1 -3 3 2 1 1 -1 0 2 0 1 0 -2 1 0 -3 -2 2 0 -1 2 2 -1 0 -1 -1 0 -2 0 0 -1 -2 0 -2 0 2 -3 -1 -1 0 -1
  4 2 0 -13 3 1 8 1 -2 5 3 -4 1 0 1 0 -4 3 0 -3 -3 -4 0 -2 1 0 0 -5 1 0 0 1 1 1 -1 2 2 1 0 -1 -2 1 -2 0 1 0 0 -1 -1 0 1 -1 0 -1 0 0
  11 12 -1 -14 -11 22 2 -3 -13 8 4 0 -2 3 1 -5 -2 13 3 -6 -9 -4 6 -1 4 -2 -7 -3 4 -1 2 -1 2 -2 -2 1 3 3 1 -2 -3 2 -1 -4 4 -4 -1 -2 -1 -1 2 -4 -3 0 -1 3
  -7 -7 4 10 6 -6 -9 4 5 -4 -1 6 -3 -4 -1 0 3 -6 0 6 7 4 -1 -1 -1 -1 2 5 -1 2 -1 -1 -1 1 2 -1 -2 -2 -1 2 4 -1 1 3 -1 1 0 0 1 0 0 2 3 0 0 1
  15 14 -10 -36 -2 5 31 4 -14 13 11 -15 10 12 2 1 -6 7 -6 -16 -14 -9 1 -1 1 -1 -2 -10 3 -1 5 4 -2 -2 -5 1 2 6 3 -4 -8 4 -1 -4 2 0 3 -1 -2 0 -2 -1 0 0 -2 -1
  -10 -10 -3 5 5 -1 -8 0 7 -2 0 3 -4 -11 4 0 -4 4 3 4 2 3 3 -1 -1 -2 -1 2 0 2 -2 -2 1 0 1 2 -1 -1 0 1 3 1 -2 1 0 -2 -2 -1 1 1 1 -3 -1 -1 1 1
  8 0 2 -19 2 4 6 5 -4 7 6 -5 2 -4 2 1 -9 8 5 -4 -1 -2 0 -3 1 1 -1 -6 1 1 -2 -2 2 2 -1 1 3 2 2 -3 -5 3 -3 -3 3 -1 -2 -1 -3 2 2 -3 -2 -1 -2 0
  13 16 -6 -27 -1 5 24 3 -15 8 10 -9 7 13 -3 -2 -1 3 -5 -11 -10 -7 2 -4 3 -1 -2 -7 4 -1 6 3 -1 -4 -3 -1 1 4 1 -3 -5 2 1 -3 1 1 3 -2 0 -1 -1 1 0 0 -2 0
  12 4 0 -18 -3 13 7 -1 -7 9 5 -5 1 -1 1 0 -8 9 3 -6 -6 -6 2 0 3 -1 -3 -8 3 -1 -1 -1 3 0 -2 4 4 1 -1 -4 -4 4 -3 -3 2 -2 -2 -1 -2 0 1 -4 -3 -2 -2 -1
  3 5 -4 -7 -1 -13 21 3 -2 3 2 -9 9 13 -2 3 2 -10 -9 -8 -1 -3 -6 0 -4 1 5 -5 -1 0 2 4 -1 0 -2 -2 0 2 2 0 -3 0 1 1 -2 2 4 1 0 -1 -3 4 3 0 -1 -3
  -6 -7 5 27 -6 4 -22 -8 8 -7 -8 11 -5 -6 -2 0 1 -2 4 8 8 4 -1 4 1 0 0 5 -3 0 -6 -5 3 2 2 2 0 -5 -2 1 5 -2 0 3 -1 -1 -4 2 1 0 2 -1 0 -1 1 0
  13 2 6 -22 3 -2 13 6 -4 8 1 -12 2 2 0 3 -4 0 1 -4 -2 -4 -4 -2 -1 4 2 -10 2 -1 -1 2 1 2 0 -1 3 2 0 -3 -8 2 -2 -3 1 1 1 0 -4 -1 0 -1 -3 0 -3 -2
  -24 -27 8 35 8 -11 -37 2 19 -15 -11 14 -13 -22 3 3 4 -7 6 20 18 15 -1 0 -4 0 2 12 -2 5 -7 -4 0 2 7 -2 -5 -5 -3 4 8 -2 1 4 -2 -1 -3 0 2 0 2 -1 0 1 1 2
  -5 -1 -3 -5 6 -10 3 2 3 0 1 -5 2 -2 3 3 -3 1 0 -2 -1 2 -2 -2 -2 1 1 -2 -3 0 0 1 -1 2 0 -1 -1 2 2 2 -3 1 -1 0 1 0 1 -1 0 0 -1 0 0 1 0 1
  0 8 -5 6 -5 5 -2 -7 -4 -3 -1 2 1 6 -2 -2 2 1 -2 -2 -5 -2 3 2 3 -1 -2 1 -1 -2 3 0 -1 -2 -1 1 -1 -1 -1 0 2 -1 2 1 -1 1 -1 1 1 -1 -1 1 1 0 1 1
  5 4 -3 -9 -7 11 5 -1 -6 7 6 -1 2 2 1 -1 -5 7 1 -6 -5 -3 2 0 2 -3 -3 -3 1 0 -1 -2 2 0 -2 2 3 1 2 -2 -2 2 -2 -2 2 -3 -1 -1 0 1 1 -2 -1 -1 -1 0
  9 7 -1 -12 1 -2 12 1 -5 5 0 -6 5 11 -2 1 1 -3 -5 -5 -4 -4 -2 2 1 0 2 -3 0 -1 2 2 -3 -1 -2 0 0 1 0 0 -2 0 2 1 -1 2 2 0 -1 -2 -2 1 2 0 -1 -1
  9 12 -8 -15 -7 9 14 -1 -9 9 5 -6 6 11 1 -2 -3 6 -3 -11 -11 -6 2 2 2 -2 -3 -4 0 -2 3 1 -2 -1 -4 1 2 3 3 -1 -4 1 0 -2 1 0 1 0 -2 -1 -2 0 0 -1 0 0
  22 17 0 -43 0 13 29 7 -16 19 12 -13 7 10 0 -4 -8 12 1 -16 -14 -11 3 -3 2 0 -2 -11 3 -2 4 1 1 0 -5 1 5 6 4 -4 -9 3 -3 -5 5 -2 2 -2 -4 1 0 -3 -3 -2 -2 0
  -7 -5 3 22 -6 3 -14 -5 6 -6 -6 7 -5 -3 -1 -1 3 -4 1 6 5 3 1 3 0 -1 0 5 -1 0 -4 -3 2 0 1 0 0 -4 -1 1 4 -2 0 2 -2 -1 -3 1 1 0 1 0 0 0 1 -1
  2 7 1 4 -7 14 -5 -4 -6 -1 1 7 -4 1 -2 -6 4 5 1 1 -2 -1 6 -1 3 -2 -4 4 3 0 2 -1 2 -3 -1 0 0 0 -1 0 3 0 1 -1 1 -3 -1 -1 2 0 1 -1 0 0 1 2
  3 0 0 -5 0 5 3 2 -2 4 3 0 2 1 -1 -2 -2 2 1 -2 -1 -2 2 1 1 -2 0 1 1 1 0 -2 0 0 -1 1 1 0 1 -1 1 0 0 0 0 -1 -1 1 0 1 0 -1 0 -1 0 -1
  -6 -10 8 14 3 -7 -9 4 7 -5 -3 5 -3 -6 -1 1 4 -8 2 7 9 5 -3 0 -3 0 3 5 -1 1 -2 0 0 2 2 -2 -1 -3 0 2 3 -1 1 1 -2 1 0 1 0 1 1 2 1 1 0 -2
  4 3 -2 -12 1 6 5 1 -4 6 4 -1 1 0 2 -2 -3 7 1 -4 -5 -3 2 -1 1 -2 -2 -2 1 0 2 1 0 0 -2 2 1 2 1 0 -1 2 -1 -1 2 -1 0 -1 -1 0 0 -1 0 -1 0 1
  -4 0 -3 -2 2 -1 4 -3 2 -1 0 -2 -1 -4 3 -1 -3 4 1 -1 -3 -1 2 -2 -1 0 0 -2 0 -1 1 1 2 0 -2 2 0 0 1 1 0 1 -2 0 0 -1 -2 -1 0 1 2 -2 0 1 1 0
  12 13 -1 -10 -10 16 5 -4 -12 5 1 -1 0 10 -1 -3 1 5 -3 -5 -7 -5 4 2 5 -2 -5 -2 4 -1 2 0 0 -4 -2 1 2 1 -1 -2 -1 1 1 -1 1 -2 0 -2 0 -2 0 -2 0 0 -1 1
  -19 -13 -1 24 5 -19 -8 -1 14 -12 -5 5 0 -7 1 4 4 -10 -3 7 10 7 -5 0 -6 1 5 6 -4 2 -2 1 0 2 2 -1 -4 -2 0 3 5 -2 1 4 -3 1 0 2 3 2 0 3 3 2 2 -1
  -5 0 -1 16 -10 12 -17 -9 1 -4 -5 5 -8 -5 3 -1 1 4 2 3 -3 0 4 3 2 -1 -5 1 0 -2 -2 -1 2 0 1 2 1 -2 -2 0 2 0 -1 0 0 -2 -3 0 0 -2 0 -2 -2 0 1 2
  -8 -12 8 14 4 -1 -18 5 8 -3 -3 9 -6 -11 0 -3 1 -1 7 9 10 7 2 -1 -2 -1 1 8 -1 3 -4 -4 1 2 2 -2 -1 -2 1 3 4 -1 0 1 0 -2 -2 0 0 1 1 -1 0 -1 1 1
  -8 7 -5 10 -5 -4 5 -6 -1 -5 0 -2 3 7 -2 0 4 -5 -5 -5 -4 -1 1 1 -1 -1 2 1 -3 -2 3 1 1 -1 -2 -1 -2 0 1 1 2 -1 2 1 -2 -1 0 1 3 1 -2 2 1 1 1 -1
  8 4 5 2 -11 10 -3 0 -8 2 2 3 0 6 -5 -1 3 -3 1 -1 1 -2 0 1 3 -1 -1 0 2 0 -1 -2 1 -1 1 -1 3 -1 -1 -3 0 -1 2 -2 0 0 0 1 0 0 0 2 -1 -1 -2 -1
  5 4 -1 -19 7 -5 16 5 -4 7 6 -9 6 4 -1 0 -3 0 -1 -7 -5 -5 -1 -2 -1 0 3 -5 0 -1 3 3 -1 1 -2 0 1 3 2 0 -3 1 0 -1 0 1 2 0 -1 0 -2 1 -1 -1 0 -2
  -9 -12 -1 10 6 -8 -10 5 9 -3 -2 3 -2 -6 4 3 0 -4 0 5 5 6 -1 3 -2 -2 0 6 -2 2 -2 -1 -4 1 2 -1 -2 -2 0 2 2 0 0 2 -1 1 1 0 0 0 -2 1 2 0 0 0
  6 6 -1 -2 -3 9 -6 -7 -3 -1 -3 1 -2 -1 0 -1 -2 8 3 1 -4 -2 3 1 4 2 -4 -2 0 -2 0 -1 0 -1 0 2 1 0 -2 -1 -1 0 0 -1 1 0 -2 0 -1 -1 1 -3 -2 0 1 2
  15 8 2 -23 -7 15 9 4 -10 13 6 -6 2 3 1 -2 -7 11 4 -8 -6 -5 2 -1 2 1 -3 -7 2 0 -2 -3 2 1 -2 0 5 4 3 -4 -7 2 -3 -5 4 -3 -1 -1 -4 1 1 -4 -4 -2 -2 1
  1 6 5 -3 0 2 3 -1 -2 1 0 -2 -2 1 -2 -1 1 -1 0 -2 -2 -3 0 -2 0 2 1 -4 0 -2 0 0 3 1 0 0 1 1 -1 -1 -1 -1 -1 0 1 -1 0 -1 0 0 1 -1 -2 0 0 1
  6 5 2 -7 -1 1 12 3 -4 5 3 -2 3 7 -3 -2 2 -3 -3 -4 -2 -4 -2 -1 -1 0 2 -3 1 -1 2 1 1 0 -1 0 1 1 1 -1 -1 -1 0 0 0 0 2 1 0 0 0 2 1 0 -1 -1
  -6 -8 1 12 -3 2 -14 0 5 -2 -5 4 -5 -5 3 1 1 0 2 5 3 5 0 3 -1 0 -1 4 -1 1 -3 -2 -1 1 2 -1 -1 -1 0 1 1 -1 0 0 0 -1 -1 0 -1 -1 0 -1 -1 0 0 1
  -7 -9 2 26 -12 6 -26 -6 4 -6 -8 10 -6 -4 1 2 3 -1 3 8 7 8 -1 5 1 -2 -3 7 -1 2 -5 -4 0 0 4 -1 0 -4 -1 1 3 -1 1 1 0 -2 -2 1 1 -1 1 0 -1 0 -1 1
  -6 -7 10 17 2 -1 -18 0 8 -5 -5 7 -5 -8 -2 -1 1 -2 7 8 8 5 0 1 0 1 1 6 -3 0 -5 -5 2 3 3 -1 0 -3 0 2 3 -3 0 1 0 -2 -2 1 1 2 1 -1 -2 0 1 0
  4 6 -7 -14 -1 4 8 3 -7 4 5 -5 4 5 2 0 -2 5 -2 -6 -6 0 3 0 2 -2 -3 0 1 1 3 0 -3 -2 -2 -1 -1 3 2 -1 -3 2 1 -2 1 -1 1 -1 0 0 -2 -1 1 1 -1 1
  19 13 -4 -30 -3 5 26 2 -14 12 7 -11 9 15 -3 0 -3 3 -4 -11 -9 -8 -2 -1 3 0 0 -9 4 -1 4 3 -1 -3 -3 0 3 3 1 -4 -7 2 0 -3 1 2 3 -1 -2 -1 0 1 -1 -1 -3 -2
  -2 -1 1 -2 1 -6 7 3 1 0 2 -2 2 0 1 0 0 -2 0 -2 1 0 -2 -2 -3 1 2 -1 0 0 1 1 1 1 0 -1 1 1 2 0 -1 -1 -1 -1 1 0 1 0 0 2 1 1 0 1 0 -1
  22 21 -2 -33 -4 11 32 0 -17 13 9 -10 9 17 -5 -5 -2 5 -4 -14 -12 -13 2 -3 4 0 0 -10 5 -3 6 3 2 -3 -6 2 4 4 1 -4 -5 1 0 -3 1 0 2 -1 -1 0 0 0 0 -1 -1 -2
  13 11 1 -17 0 4 14 0 -10 5 5 -5 4 9 -5 -1 0 0 -2 -5 -5 -7 0 -2 4 1 0 -6 3 -2 3 2 0 -2 -1 0 2 1 -2 -3 -3 0 1 -2 0 2 2 -1 0 -1 0 1 -1 -1 -1 -1
  0 1 5 15 -9 8 -12 -7 0 -3 -7 3 -5 2 -2 -1 4 -3 1 3 0 0 1 4 2 0 -1 2 0 -2 -2 -1 2 0 1 0 1 -3 -2 0 2 -2 1 1 -1 -1 -2 1 0 -2 0 0 -2 0 0 -1
  -3 -6 4 4 -3 6 -13 2 2 0 -1 3 -6 -9 4 1 -2 5 5 4 3 4 1 0 0 0 -3 2 0 1 -4 -3 1 2 2 -1 1 0 1 0 -1 1 -2 -2 2 -3 -2 -1 -1 1 2 -3 -2 1 -1 2
  8 1 2 0 -9 12 -8 -1 -4 3 -2 2 -3 1 1 0 -2 4 3 1 0 0 1 3 3 0 -4 -1 2 0 -3 -3 0 -1 1 0 3 -1 -1 -2 -2 1 -1 -2 1 0 -2 -1 -3 -1 1 -2 -2 -1 -2 1
  -11 -11 -1 6 13 -10 -11 3 10 -5 -1 4 -3 -12 3 2 -2 1 3 8 6 6 0 -2 -1 0 1 4 -2 2 -1 -1 -2 1 2 0 -3 -1 -1 3 3 1 -1 2 -1 1 -1 -1 1 1 0 -1 1 0 1 2
  56 56
  0 4 -2 6 -7 9 -4 -3 -5 -1 0 4 -1 5 -2 -3 3 0 -1 0 -2 1 4 2 3 -4 -3 5 1 0 1 -1 -1 -3 -1 -1 -1 -1 0 1 2 0 3 0 -1 -1 -1 -1 1 -1 0 0 1 0 0 0
  1 0 0 -4 5 -5 3 0 4 0 0 0 1 -3 1 1 -3 3 1 1 2 0 -2 -2 -1 3 1 -2 -1 0 -1 -1 1 1 0 1 1 1 0 0 -1 0 -2 0 1 0 0 -1 0 2 1 -2 0 0 1 1
  -6 -14 6 5 10 -7 -8 7 9 -1 -1 3 -2 -10 1 0 -2 -3 5 6 8 4 -1 0 -2 0 3 4 -1 3 -4 -2 0 3 2 0 -1 -2 0 1 2 -1 -1 1 0 1 -1 1 -1 1 1 0 0 -1 0 -1
  -7 -11 8 11 6 -4 -18 3 9 -4 -8 2 -8 -10 2 1 2 -3 5 10 6 6 0 1 -1 1 0 4 -1 0 -4 -1 -1 2 4 -2 -1 -2 -1 3 1 -1 0 1 -1 0 -1 0 -1 -1 0 -1 -2 1 0 1
  1 -2 3 -12 14 -8 3 4 5 2 -1 -7 -1 -6 2 2 -4 1 2 1 -1 -2 -2 -2 -1 3 2 -5 -1 -2 0 2 -1 3 1 1 0 1 -1 1 -3 1 -2 1 0 2 1 0 -2 -1 -1 -1 -2 0 1 0
  8 -2 4 -14 9 -8 9 6 4 5 -1 -8 2 -2 1 3 -3 -1 1 0 1 -2 -5 -1 -2 5 4 -6 0 -1 -1 2 -1 3 0 0 2 1 0 -1 -5 0 -3 -1 0 3 2 1 -3 -1 -1 0 -2 0 0 -2
  -13 -10 4 25 -1 -8 -17 -3 10 -10 -8 7 -6 -7 0 2 4 -8 1 9 9 6 -2 1 -3 1 2 4 -2 1 -3 -1 1 1 4 -1 -1 -4 -2 2 4 -2 0 3 -2 1 -1 1 1 0 1 2 0 0 1 0
  -3 -3 2 6 5 0 -13 0 5 -3 -5 4 -4 -8 2 -1 3 5 4 7 1 6 2 0 -1 1 -2 5 -2 -1 1 0 -2 1 1 -1 -3 1 1 4 2 0 1 0 0 -2 0 1 1 0 -1 -2 0 3 1 3
  19 11 0 -17 -9 13 14 0 -12 10 4 -3 4 12 -3 -3 -1 4 -1 -7 -6 -7 1 1 4 1 -1 -5 4 -1 1 0 1 -2 -3 1 4 2 0 -4 -4 -1 0 -4 2 0 1 -1 -2 -1 0 -1 -1 -2 -2 -1
  2 7 -3 1 -10 4 7 -2 -6 1 2 -1 3 10 -2 -1 3 -3 -4 -5 -3 -1 1 1 1 -3 -2 1 1 0 1 0 0 -3 -2 -2 1 0 2 0 0 0 2 -1 -1 -1 1 -1 1 0 0 1 1 1 -1 -1
  9 6 -8 -14 -8 11 13 -6 -8 8 5 -3 4 6 2 -1 -8 9 -1 -10 -8 -9 1 1 3 -1 -2 -8 3 0 0 0 3 -1 -3 6 4 1 -1 -5 -3 1 -3 -2 4 0 -2 -1 -2 0 2 -2 -1 -4 -1 0
  -1 11 -4 -6 -1 1 13 -1 -10 -1 7 -3 3 9 -5 -3 4 -4 -5 -6 -7 -5 4 -3 2 -3 0 -1 2 -2 7 3 0 -4 -2 -1 -2 1 0 0 2 0 4 0 -3 0 2 -1 3 0 -1 3 1 1 0 -1
  -5 -8 5 9 6 -8 -4 3 8 -4 -2 5 0 -6 -2 0 3 -4 2 7 9 6 -3 -2 -3 2 4 5 -1 2 -2 -1 1 2 1 -1 -2 -1 1 2 3 -2 0 1 -1 0 0 1 2 2 2 1 1 2 1 -1
  1 -7 6 -4 8 -1 -5 6 4 3 -2 -4 -4 -6 2 1 -2 -2 3 2 0 -2 0 2 0 2 1 -2 0 -1 -3 0 -1 3 2 1 0 0 -2 -1 -1 -1 -1 0 0 1 0 1 -3 -2 -2 -1 -2 -1 -1 0
  -2 0 -3 0 0 -6 11 -1 2 -1 3 0 4 2 -2 1 -2 -4 -3 -2 3 -1 -2 -2 -2 0 3 -2 0 2 -1 -1 2 -1 -1 1 1 -1 0 -1 1 0 -1 1 -1 1 0 -1 1 2 3 0 1 -1 1 -2
  2 -4 7 -2 15 -5 -3 5 7 1 -3 1 -1 -5 -2 -3 1 -1 4 6 3 1 0 0 0 1 2 4 -1 -1 0 1 -2 2 0 0 -2 -1 0 4 2 -1 1 2 -2 2 1 1 -1 -1 -1 0 0 0 2 -1
  -2 9 -7 1 -9 4 7 -10 -6 -1 1 0 1 7 0 -1 1 2 -5 -6 -7 -5 1 -1 0 -1 -1 -5 1 -2 4 3 3 -2 -1 3 1 1 -1 -1 1 0 0 1 1 -1 0 -1 2 0 1 1 0 -1 1 1
  -3 -12 10 9 8 -3 -22 3 11 -2 -10 5 -9 -14 4 0 0 3 8 12 7 6 -1 1 -2 4 0 3 -2 0 -4 -1 -1 4 4 -1 0 -1 -1 3 0 -1 -2 1 1 0 -1 1 -3 -1 0 -2 -2 0 1 3
  -4 2 -2 4 1 -4 -1 -4 2 -4 -3 -2 -3 0 1 2 2 -3 -3 1 -2 -2 0 0 0 2 0 -3 0 -2 1 2 0 -1 2 1 0 0 -3 0 1 -1 0 1 -1 1 1 -1 1 -1 -1 0 -1 0 1 1
  -9 -14 5 23 -5 -5 -16 -3 13 -6 -8 7 -5 -9 2 4 -1 -4 3 8 12 6 -5 2 -4 3 2 2 -2 3 -9 -5 4 3 4 1 2 -4 -1 -1 2 -2 -4 2 1 -1 -3 1 0 2 3 -1 -1 -1 0 0
  8 6 1 -8 -6 3 11 0 -5 5 2 -4 2 7 -1 0 -1 -2 -3 -6 -3 -7 -2 0 0 2 1 -7 2 -1 0 1 2 0 -1 1 4 1 -1 -4 -3 -1 -2 -1 1 1 1 0 -2 -1 0 1 -1 -2 -1 -1
  -14 -16 -1 13 13 -12 -18 -1 15 -8 -5 6 -4 -18 6 4 -5 3 5 9 8 7 -2 0 -3 1 1 3 -4 2 -3 -1 -1 4 3 3 -3 -2 -2 3 3 1 -2 3 1 1 -2 1 0 1 1 -2 1 0 2 2
  6 -1 12 5 -2 7 -7 4 -2 2 -2 5 -4 2 -6 -4 5 -6 3 5 5 0 1 1 2 0 1 4 2 0 -3 -2 1 0 1 -2 1 -2 -1 0 2 -3 2 0 -1 0 0 0 -1 -1 1 1 -1 -1 -1 -1
  6 9 -7 -15 -1 9 7 -5 -6 5 5 -1 2 0 3 -2 -7 14 1 -7 -8 -6 3 -2 2 0 -4 -6 1 -1 3 0 2 0 -2 5 2 3 0 -2 -2 2 -3 -1 5 -2 -1 -1 0 1 1 -3 -1 -2 1 3
  -5 3 -1 11 -8 4 -2 -2 -6 -5 2 6 -1 5 -4 -3 7 -5 -3 1 1 2 4 -1 1 -4 -1 5 2 1 3 0 1 -4 0 -2 -2 -1 0 1 5 -1 4 0 -2 -2 0 -1 4 1 1 2 2 1 -1 0
  15 13 -6 -24 -4 2 26 0 -12 9 8 -10 10 13 -3 1 -2 2 -5 -12 -8 -7 -2 -2 1 0 1 -9 2 -1 4 3 0 -2 -4 1 2 3 2 -3 -5 2 0 -3 1 1 3 0 0 0 0 1 0 0 -2 -2
  8 0 7 -12 9 2 1 7 -1 4 2 1 -1 -4 -2 -3 -1 4 5 4 3 0 1 -3 2 3 1 1 2 0 0 -1 0 1 0 -1 0 2 0 0 -1 -1 0 -2 1 0 0 -1 -1 1 1 -2 -1 0 0 1
  6 2 1 3 -3 5 0 -1 -1 2 1 5 4 4 -4 -2 0 1 1 0 3 1 -1 2 2 -1 0 4 -1 1 -2 -3 0 0 -2 0 0 -1 1 0 1 0 1 0 0 0 -1 1 0 1 1 0 2 -1 0 -1
  -5 -8 3 -8 15 -3 -8 4 5 -1 1 -1 -4 -14 4 0 -6 7 7 4 1 1 2 -3 1 1 -1 0 0 0 -1 0 0 3 2 2 -2 1 -1 1 0 1 -1 0 2 0 -2 -1 -1 1 1 -3 -2 0 1 2
  5 6 -2 -9 -4 4 9 1 -5 5 1 -7 1 8 1 0 0 -1 -3 -6 -7 -4 1 2 1 -1 -1 -3 1 -2 1 1 -1 -1 -1 0 2 1 1 -1 -3 0 0 -1 0 0 1 -1 -1 -1 -2 0 -1 0 -1 -1
  10 9 -4 -7 -12 10 12 -1 -10 7 4 -3 6 14 -2 -2 1 0 -4 -9 -6 -4 1 3 2 -3 -2 -1 2 0 1 0 0 -2 -3 0 2 1 2 -2 -2 0 1 -2 1 -1 1 0 0 -1 -1 1 1 -1 -2 -2
  9 6 2 -11 3 0 8 2 -3 4 0 -5 1 4 -1 0 1 0 -1 -2 -4 -4 -1 0 1 3 1 -4 1 -3 2 2 -1 0 -1 0 1 2 -1 -1 -3 -1 0 -2 0 1 2 0 -1 -1 -2 0 -1 1 -1 0
  7 6 -4 -2 -3 13 -3 -5 -1 4 1 6 3 -1 1 -4 -4 14 4 -2 -3 1 3 2 2 -2 -5 4 -2 0 0 -3 0 1 -4 3 0 1 3 2 1 2 -1 0 3 -3 -2 1 0 1 1 -4 1 0 2 2
  -14 -8 6 34 -12 -3 -24 -4 7 -11 -11 7 -8 -1 0 3 8 -12 -1 8 8 8 -2 5 -3 0 0 7 -3 0 -5 -2 0 1 5 -4 -1 -4 -1 2 3 -3 2 3 -2 -1 -1 1 1 -1 -1 3 0 1 0 0
  4 10 2 2 -5 8 3 -1 -8 0 3 4 0 8 -6 -6 5 -2 -1 -1 -2 -3 4 -1 4 -1 -1 3 2 -2 3 0 1 -3 -2 -2 0 0 0 0 2 -2 3 -1 -2 0 0 -1 1 0 0 2 1 0 0 0
  -4 -9 3 5 5 1 -8 0 6 0 0 5 -2 -9 1 -1 -4 3 5 3 4 0 0 0 0 0 1 1 -1 1 -4 -3 3 3 1 4 0 -1 -1 -1 3 -1 -2 1 2 -1 -3 1 0 2 2 -2 0 -2 0 1
  11 4 2 -12 6 1 0 -3 1 4 -3 -2 0 -3 1 1 -5 9 4 1 -2 -3 -3 -1 1 5 0 -7 -1 -3 0 1 0 3 0 3 2 1 -1 0 -4 1 -3 0 3 2 0 1 -3 -1 1 -2 -2 -1 1 2
  3 -2 5 -5 3 11 -10 3 -4 3 1 1 -7 -3 -1 -3 -2 2 4 4 -2 -3 6 1 6 -3 -4 1 3 0 -2 -2 -1 -2 2 0 1 -2 -3 -1 1 1 1 0 -1 0 -2 -2 -2 -2 0 -2 -2 -3 -1 1
  5 3 4 -18 8 -2 12 6 -4 5 6 -7 2 1 -2 -1 -3 0 1 -4 -2 -5 0 -4 1 1 2 -5 2 -1 1 1 2 1 0 0 1 2 0 -2 -3 0 -1 -1 1 0 1 -1 0 1 0 0 -2 -1 -1 -1
  9 12 -13 -21 -4 9 24 -2 -13 8 11 -5 10 11 -1 -4 -4 8 -4 -13 -12 -8 4 -1 3 -5 -2 -3 3 0 7 3 -1 -4 -7 3 0 2 3 -2 -1 3 1 -2 0 1 0 0 0 0 0 1 2 -1 0 -2
  -15 -16 5 25 8 -15 -23 4 15 -12 -8 8 -6 -13 2 4 4 -8 2 14 14 12 -3 1 -4 2 2 9 -4 3 -4 -2 -3 2 5 -4 -4 -3 -1 4 4 -1 1 3 -3 1 0 1 1 0 -1 1 2 2 1 1
  0 -1 8 9 -6 7 -12 1 -3 -2 -1 4 -5 -1 -4 -1 4 -4 3 4 4 2 2 0 2 0 -1 2 1 0 -3 -3 2 0 3 -2 0 -1 -1 -1 2 -2 2 -1 0 -2 -1 0 1 0 1 0 -2 0 -2 1
  16 9 1 -9 -10 7 6 -7 -3 6 -4 -2 2 5 0 1 -4 8 2 -3 -2 -3 -4 0 0 5 -1 -9 0 -2 -2 -1 3 1 -1 2 6 1 1 -2 -6 0 -4 -2 4 0 0 0 -3 0 3 -3 -3 -1 0 1
  3 6 -2 5 -14 9 -2 -8 -7 -1 -3 2 -3 7 -1 0 4 0 -3 0 -3 -1 1 1 2 -1 -3 -2 3 -1 1 1 1 -4 1 0 2 -1 -2 -1 0 0 1 -1 0 -1 0 -2 1 -1 2 0 -1 0 -1 1
  -1 -1 2 10 -10 1 -5 -2 -1 -3 -3 2 -2 2 -1 2 4 -4 -1 2 4 3 -2 0 -1 1 0 0 1 1 -2 -1 2 -1 2 -2 1 -1 0 -1 0 -1 0 -1 0 -1 0 0 1 0 1 1 -1 1 -2 0
  -1 -7 3 2 -3 5 -11 4 2 3 -2 -1 -3 -4 4 1 -2 2 4 1 0 3 1 4 0 -2 -3 3 -1 1 -4 -2 -2 2 1 -2 1 -1 2 0 -2 1 -1 -1 1 -1 -1 1 -3 -1 -1 -1 -2 0 -1 0
  -1 -17 14 3 13 -9 -18 9 14 -1 -7 1 -7 -18 3 4 -3 0 9 13 13 7 -5 -1 -3 6 3 1 -2 2 -8 -3 0 6 5 -2 1 -1 -1 1 -2 0 -4 0 1 0 -1 1 -3 1 1 -3 -3 0 0 1
  7 7 -7 -22 5 4 17 -1 -6 7 9 -6 6 1 1 -1 -9 9 0 -10 -9 -9 2 -2 2 -1 -1 -8 1 -1 3 1 1 0 -4 5 1 2 0 -3 -2 3 -2 -1 2 1 -1 0 -2 1 1 -2 0 -2 0 0
  10 11 -5 -21 -3 4 17 3 -10 8 6 -10 6 10 0 0 -1 3 -3 -10 -10 -4 2 0 1 -2 -2 -4 1 -1 4 2 -3 -2 -3 -2 1 3 3 -1 -5 2 1 -3 1 0 3 0 -1 -1 -2 0 -1 1 -1 -1
  0 0 -1 -3 -3 1 2 1 -2 1 0 -5 -1 2 2 2 0 -2 -2 -2 -3 -1 0 1 0 -1 -1 -2 1 -1 0 1 -1 -1 0 -1 1 0 0 -1 -2 1 0 -1 -1 0 0 -1 -1 -1 -1 0 -1 1 -1 -1
  15 10 -1 -21 3 8 11 1 -7 9 4 -3 4 5 -2 -3 -3 9 1 -4 -6 -4 2 -1 3 0 -2 -3 1 -1 2 0 -1 -1 -3 1 1 3 1 0 -3 2 0 -2 2 -1 1 -1 -1 0 0 -3 0 -1 0 1
  0 -5 4 12 2 -1 -11 -1 7 -4 -5 9 -3 -5 -2 -1 1 -1 3 9 9 5 -1 0 0 1 1 5 -1 2 -3 -3 0 0 1 0 0 -3 -1 2 3 -1 0 2 -1 1 -1 0 0 0 2 -1 1 -1 2 0
  7 2 2 -12 8 -2 3 3 2 4 0 -3 1 -3 2 0 -3 6 3 0 -1 -1 -1 -1 0 3 0 -2 -1 -1 0 1 -1 2 -1 0 1 2 1 1 -3 1 -2 -1 2 1 1 0 -2 0 -1 -2 -1 0 1 1
  4 8 4 5 -13 15 -5 0 -10 1 0 2 -5 8 -3 -4 7 -3 -1 -1 -4 -2 5 2 4 -2 -4 3 3 -2 1 -1 0 -3 0 -3 1 0 0 -1 1 -2 3 -2 -1 -2 0 -1 0 -2 -1 1 -1 1 -2 1
  -14 -5 -2 11 7 1 -13 0 5 -6 0 5 -4 -10 3 -3 1 3 3 3 -1 4 6 0 0 -4 -3 8 -2 0 2 0 -1 1 0 1 -5 0 1 4 6 0 2 2 0 -2 -2 1 2 0 -1 -1 1 2 2 2
  -9 -14 2 17 6 -2 -17 0 13 -5 -5 9 -2 -13 3 0 -2 2 6 7 8 7 -1 3 -2 0 1 8 -3 2 -4 -3 0 5 1 3 -3 -2 0 2 4 -2 -1 2 2 0 -3 3 0 1 1 -1 1 0 2 0
  56 56
  0 4 1 5 -4 7 -4 0 -5 -1 2 5 -3 4 -3 -4 3 -2 0 2 -1 -2 4 0 4 -2 -3 3 2 -1 1 -1 0 -3 1 -1 1 -1 -1 0 3 -2 2 0 -2 0 0 -2 1 -1 0 1 0 -1 0 1
  -3 0 -1 7 -1 -1 -4 -1 1 -3 0 2 1 -1 0 0 2 0 0 0 1 2 0 1 -1 0 0 3 -2 0 1 0 -1 1 0 -1 -2 0 1 1 1 0 1 0 0 0 0 2 1 0 -1 1 1 1 1 0
  6 2 3 -12 0 3 8 2 -4 5 3 -3 1 1 -1 0 -2 1 0 -3 -1 -3 -1 -2 0 0 1 -5 2 0 0 0 2 0 -1 1 2 1 0 -2 -2 1 -1 -1 1 -1 0 -1 -1 1 2 -1 -1 0 -1 -1
  3 4 -1 -13 2 -2 15 1 -3 4 5 -4 4 3 0 -1 -2 1 -1 -6 -4 -5 -1 -3 -1 0 2 -5 1 -1 3 2 2 0 -2 2 2 2 1 -1 -1 0 -1 -1 1 0 1 -1 0 2 1 0 0 0 0 -1
  -14 -16 4 20 4 -14 -15 0 15 -8 -9 2 -4 -10 3 5 1 -8 2 8 9 7 -5 2 -5 2 4 3 -4 1 -5 -1 0 4 4 0 -1 -3 -1 2 2 -2 -1 3 -1 1 -1 2 0 1 0 1 0 1 1 -1
  -7 -7 -1 -4 8 -7 0 2 5 -1 2 -2 1 -9 3 1 -5 3 4 -1 1 1 0 -3 -2 0 2 -1 -1 1 0 0 1 3 0 2 -1 1 1 0 0 0 -1 0 2 0 -1 1 0 2 1 -1 -1 0 1 0
  2 2 3 -8 1 -4 12 3 -1 3 3 -4 3 4 -1 0 0 -4 -2 -4 0 -3 -2 -2 -2 1 3 -3 1 0 0 1 2 1 -1 0 2 1 1 -1 -1 -1 -1 0 1 0 1 -1 0 2 1 1 0 0 0 -2
  16 23 -12 -29 -8 12 30 -5 -18 12 11 -10 11 17 -1 -4 -4 11 -5 -19 -18 -12 3 -1 3 -2 -3 -9 2 -3 8 4 0 -3 -7 2 2 5 3 -3 -6 3 0 -4 3 0 2 0 -1 -1 -1 0 0 -1 -1 0
  2 -1 3 0 5 9 -13 1 -1 0 1 8 -3 -8 -1 -4 -2 9 7 5 2 2 4 -1 4 -1 -3 5 0 0 0 -3 -1 1 0 1 -2 0 0 1 2 0 1 0 1 -1 -2 1 0 0 1 -2 0 0 1 3
  -7 -11 1 10 4 -7 -10 1 8 -6 -4 3 -3 -8 3 4 1 -3 0 7 7 5 -3 1 -2 1 1 3 0 2 -2 0 -1 1 3 0 -2 -1 -2 1 2 0 0 1 -1 0 0 0 1 0 0 -1 1 1 0 0
  -5 -10 7 11 6 -2 -13 3 7 -4 -2 9 -4 -9 -3 -1 0 -2 5 9 10 5 0 -1 0 0 2 6 -1 2 -4 -4 1 1 2 0 -1 -3 -1 1 4 -1 0 2 -1 0 -2 0 1 2 2 0 0 -1 1 0
  10 8 -1 -9 -7 6 6 -2 -7 5 -3 -8 1 10 0 1 1 0 -4 -4 -6 -4 -1 3 2 2 -2 -5 2 -2 0 2 -1 -1 0 -1 2 2 -1 -2 -5 0 0 -1 0 0 1 0 -2 -3 -2 0 -1 0 -2 0
  22 25 -12 -44 -8 20 32 -3 -24 17 14 -15 10 16 1 -4 -8 17 -3 -22 -23 -15 5 -2 6 -3 -6 -13 5 -4 9 5 0 -3 -8 3 3 7 3 -5 -9 5 0 -6 4 -1 1 -1 -3 -2 -1 -2 -2 -1 -2 0
  0 -12 10 7 2 -4 -11 1 9 -1 -8 3 -5 -10 0 3 -2 -2 5 8 10 4 -5 0 -3 4 4 -2 -1 2 -7 -3 3 3 3 1 2 -2 -2 -1 -1 -1 -3 1 1 0 -2 1 -2 1 3 -2 -2 -1 -1 0
  2 -1 5 5 -5 2 -5 -1 -2 -1 -2 1 -3 3 -4 1 2 -6 0 3 3 -1 -1 1 2 1 0 -1 2 0 -3 -1 1 -1 3 -1 2 -2 -3 -2 0 -2 1 0 -1 1 0 -1 0 -1 1 1 -2 -2 -1 -1
  -4 -5 0 -7 5 -10 10 5 4 3 2 -8 5 -1 3 2 -3 -3 -1 -6 -1 -1 -4 0 -5 0 4 -3 -2 0 0 2 0 4 -1 0 0 2 3 0 -3 0 -1 0 1 0 1 2 -1 1 -1 1 0 1 0 -3
  12 16 -5 -19 -3 5 22 0 -10 9 7 -7 8 15 -3 -3 -2 3 -4 -12 -11 -8 1 0 2 -1 -1 -4 0 -3 4 2 -1 -1 -5 0 2 2 3 -1 -4 1 0 -1 1 1 2 0 -1 0 -2 2 1 -1 0 -1
  5 8 -3 -20 6 -4 25 4 -5 7 11 -5 9 5 -2 -3 -3 2 -2 -10 -5 -6 0 -5 -2 -2 3 -4 0 0 5 2 1 0 -5 1 1 2 4 0 -1 2 -1 -1 1 0 2 0 1 3 1 1 2 0 1 -2
  -5 -6 5 11 2 -6 -4 1 7 -3 -4 3 -1 -2 -1 0 3 -6 0 3 5 2 -3 1 -3 2 4 3 -2 0 -2 0 1 3 1 0 -1 -1 0 1 2 -3 0 2 0 1 0 2 0 1 0 2 1 0 1 -1
  1 -1 1 -2 0 0 1 0 0 0 1 0 1 -2 0 0 -1 2 2 -1 1 1 0 -1 -1 0 1 0 0 1 0 0 1 0 -1 0 0 0 1 0 0 1 0 -1 1 0 -1 0 0 1 1 -1 -1 0 0 -1
  -15 -20 5 18 11 -15 -19 2 19 -9 -7 7 -5 -19 4 5 -3 -2 6 12 14 10 -4 -1 -5 3 4 5 -4 4 -7 -4 1 5 4 1 -2 -3 -1 2 3 -1 -3 3 1 0 -2 1 1 3 2 -2 0 0 2 1
  1 -1 5 0 1 -1 1 2 1 1 0 0 -1 0 -2 1 1 -4 -1 1 3 -1 -2 0 -1 1 2 -1 0 0 -2 -1 1 1 1 0 1 -1 -1 -1 0 0 -1 1 0 0 0 0 0 1 1 1 0 0 0 -1
  6 0 1 -14 4 2 5 3 -2 6 2 -4 2 -1 1 0 -4 5 2 -2 -2 -2 -1 -1 1 0 0 -3 1 0 0 0 0 1 -1 1 1 2 1 -1 -3 1 -1 -1 1 -1 0 0 -1 0 0 -2 -1 0 -1 0
  -21 -19 4 36 8 -11 -31 0 20 -13 -11 12 -7 -15 2 2 5 -6 4 15 13 14 -1 4 -4 0 2 15 -7 2 -6 -4 -3 4 4 -2 -6 -5 0 6 7 -2 1 5 -2 0 -2 3 2 1 -1 1 2 2 3 1
  16 15 -3 -24 -1 8 17 -1 -10 10 3 -8 5 11 -1 -1 -2 7 -3 -8 -10 -7 0 0 3 2 -2 -7 2 -3 3 2 -1 -1 -3 1 2 4 0 -2 -6 1 -1 -2 2 0 2 -1 -2 -1 -1 -1 -1 0 -1 1
  -10 -11 -4 17 1 -5 -15 -5 9 -7 -8 3 -2 -6 3 4 1 -1 0 6 4 7 -2 4 -1 -1 0 5 -2 1 -2 0 -2 1 2 1 -4 -2 -2 2 2 0 1 2 -1 0 -1 2 1 -1 -1 0 1 1 0 0
  17 15 -1 -30 -1 11 20 3 -14 13 10 -8 7 8 -2 -4 -5 10 1 -12 -10 -9 2 -3 3 0 -2 -8 2 -2 4 1 1 0 -4 1 3 5 3 -3 -6 2 -1 -4 3 -1 1 0 -2 0 0 -1 -2 -1 -1 0
  -2 -4 2 12 -6 1 -10 0 1 -3 -3 3 -3 0 0 2 3 -5 -1 4 4 3 -1 3 0 -1 -1 2 0 1 -2 -1 -1 -1 2 -2 0 -2 -1 0 1 0 1 0 -2 0 0 0 0 -2 -1 1 0 0 -1 -1
  2 3 2 -2 0 2 1 0 -1 2 -1 -2 0 1 0 -1 1 1 0 -2 -3 -1 0 1 -1 0 0 -1 -2 -2 1 1 0 1 -1 0 0 1 1 1 -1 1 0 0 0 -1 0 1 -1 0 -1 0 0 1 0 0
  -12 -10 0 21 2 -5 -15 0 8 -8 -4 9 -3 -6 0 -1 4 -4 2 8 7 7 1 1 -1 -1 1 9 -2 1 -1 -2 -1 0 2 -1 -3 -2 0 3 6 -3 2 2 -2 0 -1 1 2 1 0 1 2 1 1 1
  -4 -10 2 7 4 2 -17 1 7 -2 -4 5 -5 -11 4 1 -3 5 6 7 4 5 1 2 1 0 -2 4 -1 1 -4 -3 -1 2 2 1 -1 -1 -1 1 1 0 -1 0 1 -1 -2 0 -1 0 0 -3 -1 0 0 2
  3 5 -5 -11 1 5 6 -2 -3 3 4 -1 3 -2 2 -1 -5 10 1 -5 -4 -3 1 -2 1 1 -1 -3 0 0 2 -1 1 1 -2 3 0 3 1 -2 -2 1 -2 -1 3 -1 -1 1 0 1 1 -2 0 0 1 2
  -21 -27 2 34 9 -16 -33 2 21 -13 -12 8 -7 -17 4 7 3 -9 3 17 15 15 -4 6 -4 -1 2 13 -5 4 -7 -2 -6 3 6 -3 -6 -6 -2 5 5 0 2 4 -4 2 -1 3 1 -2 -2 1 1 1 1 -1
  6 9 -1 -11 -2 5 10 3 -8 5 5 -3 1 7 -1 -4 1 2 -1 -4 -6 -4 4 -2 2 -1 -2 -1 2 -1 3 1 0 -3 -2 -2 2 2 2 0 -1 0 0 -2 0 -1 1 -2 0 0 -1 0 0 0 -1 1
  15 10 3 -24 -1 8 16 5 -10 10 7 -7 5 6 -1 -2 -3 5 0 -8 -5 -7 0 -2 2 1 -1 -6 3 -1 2 1 1 1 -3 0 3 4 2 -3 -5 1 -1 -3 2 -1 1 0 -2 0 0 -1 -1 0 -1 -1
  2 1 0 6 -9 2 0 -4 0 0 -2 2 2 3 -1 2 0 0 -1 -2 2 2 -3 2 -2 0 1 -1 -2 1 -2 -2 2 0 -1 0 1 -1 1 -1 -1 1 -1 0 1 -1 -1 1 0 1 1 0 0 0 -1 -1
  -6 -7 -1 2 8 -10 -2 1 8 -1 -2 -2 2 -5 2 3 -2 -1 1 1 2 3 -3 1 -3 0 3 1 -4 0 -1 0 -2 3 0 1 -2 -1 1 2 0 1 -1 2 0 1 0 2 0 1 -1 1 1 1 1 -1
  -2 -5 11 7 7 -6 -7 5 5 -3 -5 3 -6 -3 -3 -1 6 -9 1 9 6 2 -1 -1 -1 2 3 2 0 -1 -1 0 0 0 3 -2 0 -2 -2 2 3 -3 1 2 -3 1 1 -1 0 0 0 1 0 1 0 0
  -14 -13 3 22 5 -9 -22 -2 16 -9 -11 4 -5 -13 5 4 1 -1 4 9 7 10 -3 3 -4 2 1 6 -6 0 -4 -2 -1 5 3 0 -3 -2 0 4 2 -1 -1 3 0 -1 -2 3 0 1 -1 -1 0 3 2 1
  -1 0 -4 -11 4 -3 9 4 -3 3 5 -6 4 2 0 0 -3 0 -1 -5 -3 -1 2 -1 0 -2 0 -1 1 1 1 1 -1 -1 -1 -1 -1 2 1 -1 -2 1 1 -1 0 0 1 -1 0 0 -1 0 -1 -1 -1 -1
  -6 -1 2 10 0 -4 -3 -1 3 -5 -2 2 -3 -2 0 0 4 -5 -2 3 3 1 0 -1 -2 1 1 1 0 0 0 1 1 0 1 -1 -1 -1 -1 1 2 -1 0 1 -1 0 0 0 1 0 1 1 1 1 1 0
  12 4 4 -8 -3 7 -1 -3 -3 5 -6 -3 -2 3 0 1 0 4 1 1 -3 -2 -2 2 2 3 -1 -5 1 -2 -1 1 0 0 0 1 2 1 -2 -1 -4 0 -1 -1 1 0 0 0 -3 -2 0 -2 -2 0 -2 1
  -15 -17 1 22 8 -13 -18 0 14 -10 -4 9 -1 -12 1 3 1 -4 4 10 12 10 -3 1 -3 -1 3 10 -4 3 -3 -2 -2 3 3 0 -4 -4 0 4 6 -1 1 3 -1 1 -1 2 3 2 1 1 2 1 2 -1
  10 16 -6 -24 5 6 24 1 -12 8 12 -4 7 11 -4 -7 -2 6 -2 -10 -12 -11 5 -4 5 -2 -1 -3 3 -3 8 3 0 -3 -5 2 1 3 1 -1 0 0 1 -2 0 1 2 -2 1 1 -1 1 1 -2 1 0
  7 4 -4 -14 2 0 9 -3 -1 4 0 -6 4 1 3 2 -5 7 0 -5 -5 -3 -2 0 0 2 0 -6 0 -1 1 2 0 1 -2 3 1 2 0 -1 -4 2 -2 -1 2 1 0 0 -2 0 0 -2 -1 0 0 0
  -9 -11 2 1 12 -13 -3 5 8 -4 -1 -1 -3 -10 2 3 0 -4 1 6 5 4 -1 -3 -3 0 3 1 0 2 0 1 -1 0 2 -1 -2 -1 -1 2 2 1 0 1 -2 0 1 -1 1 1 0 -1 0 1 0 0
  -15 -15 0 17 12 -15 -14 -1 15 -9 -6 5 -3 -14 2 3 1 -3 3 10 8 8 -2 -1 -4 0 4 5 -4 2 -1 0 -1 2 2 1 -4 -3 -1 4 5 0 0 3 -2 1 -1 2 2 1 0 0 1 1 2 0
  -1 -8 8 13 -2 -5 -12 -2 7 -4 -10 1 -5 -3 -2 5 2 -8 0 8 9 4 -5 3 -2 4 3 -1 -1 1 -7 -2 1 1 4 -1 1 -3 -4 -1 -1 -1 -1 2 -1 1 -1 0 -1 -1 1 0 -2 -1 -1 -1
  -7 -2 -2 7 1 1 -8 -2 0 -4 -1 3 -4 -2 0 -1 2 -1 0 3 -1 1 3 0 2 -2 -2 3 1 0 1 0 -1 -2 2 0 -2 -1 -2 1 3 -1 2 1 -1 0 0 -1 1 -1 0 0 0 0 0 2
  -5 0 -3 5 2 -2 -4 -2 1 -5 0 3 -2 -3 0 -1 1 1 1 3 0 1 3 -2 1 0 -1 2 0 0 2 0 0 -2 1 0 -1 0 -1 1 3 -1 1 0 -1 0 0 -1 2 0 0 -1 0 0 1 2
  1 4 0 7 -4 8 -8 -2 -3 0 -1 4 -2 3 -2 -3 3 1 1 1 -3 0 3 3 3 -2 -3 4 -1 -2 1 -1 -2 -1 0 -1 -1 -1 0 1 1 -1 2 0 -1 0 0 1 0 -2 -2 1 0 0 0 1
  -16 -10 2 27 1 -3 -21 0 7 -10 -3 11 -5 -6 -1 -2 6 -7 2 9 7 7 3 2 0 -4 -1 12 -2 1 -1 -2 -2 0 3 -2 -4 -4 0 4 8 -3 4 3 -3 0 -1 1 3 0 0 2 2 1 2 0
  -5 -9 1 0 10 -11 0 5 8 -1 0 -2 3 -7 2 3 -1 -2 1 1 4 4 -4 0 -4 0 4 2 -3 1 0 1 -2 4 0 0 -3 0 2 2 0 1 0 1 0 1 1 3 0 1 -1 1 1 2 1 -2
  -9 -14 2 16 4 -7 -15 0 10 -7 -7 7 -5 -10 2 2 2 -3 2 11 10 7 -2 0 -2 1 2 5 0 3 -3 -1 0 0 3 0 -2 -2 -2 2 4 -1 0 2 -2 0 -1 0 1 0 1 -1 1 0 0 1
  5 -3 5 -3 -3 1 3 2 1 4 -2 -1 -1 1 0 2 -1 -3 -1 0 3 -1 -4 1 -2 2 2 -4 1 1 -4 -1 2 1 1 1 3 0 -1 -2 -2 0 -2 0 1 0 0 -1 -2 0 2 -1 -1 -1 -2 -1
  -3 -5 4 5 -3 8 -12 0 1 0 0 6 -5 -7 1 -1 -3 4 5 3 3 2 2 0 1 -1 -2 2 0 1 -4 -4 2 1 1 1 1 -1 0 -1 1 0 -1 0 2 -2 -3 -1 -1 1 3 -2 -2 -1 0 1
  

• PROPERTIES
  Unimodular=1
  

• REFERENCES
  G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
  

• NOTES
  CycloQuaternionic lattice of type Delta2
  The automorphism group contains the group SL_2(29) \circ tilde(S)_3
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe