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 13:14:52 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME (required)
DIMENSION (required)
GRAM
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
REFERENCES
URL (links to other sites for this lattice)
LAST_LINE

• NAME (required)
  (U5(2) x 2^(1+4)_-.Alt_5).2
  

• DIMENSION (required)
  40
  

• GRAM
  40 0
  4
  1 4
  1 2 4
  1 2 1 4
  1 2 0 1 4
  1 1 1 2 1 4
  1 1 2 2 0 1 4
  1 1 2 1 0 1 2 4
  1 1 2 1 0 0 2 2 4
  1 1 1 1 1 2 1 2 2 4
  2 1 2 1 0 1 1 1 2 1 4
  2 2 2 1 2 2 1 1 1 2 1 4
  1 2 1 1 1 1 1 1 2 2 2 1 4
  1 0 1 1 1 1 2 2 1 1 2 1 1 4
  1 2 1 2 1 2 1 1 1 1 2 1 2 1 4
  1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 4
  1 1 2 1 0 2 1 2 2 2 2 1 2 1 2 2 4
  1 1 1 2 1 2 1 1 1 2 2 2 1 2 1 2 1 4
  1 1 1 1 1 1 2 2 2 2 1 2 1 2 2 1 1 1 4
  1 1 1 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 4
  1 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 4
  -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 4
  -1 -1 -1 0 -1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 -1 -1 1 2 4
  -1 0 -1 0 0 0 -1 -1 -1 0 -1 0 -1 -1 0 -1 -1 0 0 0 1 2 2 4
  0 0 0 0 -1 -1 0 0 0 -1 1 -1 0 0 1 0 0 0 0 -1 1 1 0 0 4
  0 -1 -1 -1 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 1 1 1 0 2 4
  -1 0 0 0 -1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 -1 0 1 2 2 1 1 1 4
  0 0 -1 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 2 1 4
  0 -1 -1 0 -1 -1 0 0 -1 -1 -1 -1 -1 0 -1 0 -1 0 -1 -1 1 0 1 0 1 2 1 2 4
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 2 1 2 1 4
  0 0 0 0 0 0 0 1 -1 0 -1 0 -1 0 0 1 0 0 0 0 2 1 0 0 1 1 1 1 2 1 4
  -1 0 0 0 0 0 0 0 -1 0 -1 0 -1 0 0 0 -1 0 0 0 1 2 1 2 0 0 2 0 1 1 2 4
  0 -1 0 0 -1 0 0 0 -1 -1 0 -1 -1 0 0 0 0 0 -1 -1 2 1 1 0 2 1 1 0 2 1 2 1 4
  0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 2 1 1 1 1 1 1 1 2 2 1 2 4
  0 -1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 -1 1 1 1 1 1 2 0 1 2 2 1 1 2 2 4
  0 0 0 0 -1 0 0 0 0 0 1 -1 0 0 1 0 1 0 0 0 2 1 1 1 2 2 2 1 0 2 0 0 1 1 1 4
  0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 2 1 2 1 2 1 1 0 1 1 1 4
  0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 1 1 1 2 2 1 1 1 2 1 1 1 2 2 1 2 4
  0 0 -1 0 0 0 -1 -1 -2 -1 -1 0 -1 -1 0 0 -1 0 -1 -1 1 0 1 1 1 1 1 2 2 1 2 1 1 1 1 0 1 2 4
  -1 -1 -1 -1 0 -1 -1 -1 -1 0 -1 0 -1 0 -1 -1 -1 0 0 0 1 2 1 2 0 1 1 1 1 1 1 2 0 0 1 0 0 0 1 4
  

• DIVISORS (elementary divisors)
  1
  

• MINIMAL_NORM
  4
  

• KISSING_NUMBER
  39600
  

• HERMITE_NUMBER
  4
  

• GROUP_ORDER
  2^18 * 3^6 * 5^2 * 11
  

• GROUP_NAME
  (U5(2) otimes 2^(1+4)_-.Alt_5).2
  

• GROUP_GENERATORS
  12
  40 40
  0 -2 1 0 1 0 1 1 -1 -1 1 -1 1 -3 0 0 -1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 2 0 1 0 0 0 -1 -1 0 -1 2 -2 0 0 -1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 -1 1 0 0 0 1 -1 0 2 2 0 0 -1 0 0 -2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 -1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 -1 0 1 0 0 1 0 0 0 0 0 1 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 0 -1 1 0 0 1 0 1 2 -1 2 0 0 0 -2 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 2 0 0 1 -1 0 0 -1 -2 -2 1 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 0 0 0 -1 0 -1 -2 1 -1 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -2 2 0 1 0 0 1 -1 -1 -1 -2 2 -2 0 -1 -1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -3 4 -1 2 0 0 0 -1 -2 -3 -4 3 -3 1 -1 -1 4 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 0 1 -1 -3 -3 1 0 1 -1 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -2 3 -1 1 0 0 0 -1 -1 -2 -3 2 -2 1 -1 -1 3 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 2 0 1 0 0 0 0 -1 -1 -1 1 -1 1 0 -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 1 0 1 0 0 1 -1 -1 0 -1 1 -1 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 3 -1 0 1 -1 -1 0 0 -3 -4 1 0 1 -1 -1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 0 0 1 -1 0 0 -1 -1 -2 1 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 1 0 -1 0 0 0 0 1 0 -1 0 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -2 -1 -1 -2 1 1 -1 0 1 0 0 -1 3 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -2 -1 -2 1 1 -2 -1 1 1 0 -1 4 0 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 -1 0 0 0 -1 0 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 -1 -1 -1 -1 1 1 -1 0 0 1 0 -1 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -1 -1 -1 -2 1 1 -1 0 1 1 -1 -1 3 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 -1 -2 -2 0 2 0 1 0 0 -1 -1 3 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 0 1 -1 0 0 1 -2 1 -1 0 0 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 -1 -2 -1 -1 0 1 -1 0 0 1 0 -1 3 0 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 -1 -1 0 -1 1 0 2 -2 0 -1 0 1 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -1 0 0 0 0 1 -1 1 -1 0 1 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 0 -1 1 0 1 -1 0 -1 0 1 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 1 2 0 -1 0 1 -1 0 0 1 -2 0 -1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 0 1 0 0 0 1 -1 1 -1 0 0 0 1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -3 -3 -3 1 2 -2 0 0 2 -1 -2 5 1 3 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 5 -2 -3 -4 -4 -5 1 4 -3 -1 1 2 -1 -3 8 1 4 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 -1 0 -1 0 1 -1 -1 1 0 1 -1 2 0 0 1 0
  40 40
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 4 -2 -3 -4 -3 -5 1 4 -3 -2 1 2 0 -3 7 1 4 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -1 -1 -2 -1 1 1 -1 0 0 0 -1 0 2 0 2 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -1 -2 -2 -1 0 1 -1 0 -1 1 -1 0 2 1 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -1 -3 -3 1 2 -1 0 1 0 0 -1 4 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -1 -1 -1 -2 1 1 -1 -1 1 0 0 -1 2 0 1 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 3 -1 -3 -3 -3 -5 2 2 -3 -1 2 2 0 -2 7 0 3 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 0 -2 -2 -3 -3 1 2 -1 0 0 1 -1 -1 4 1 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 -2 -1 -1 0 1 -1 1 -1 1 -1 0 2 1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -1 -2 -2 -2 0 2 -1 0 -1 1 -1 -1 3 1 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -1 -2 -1 -2 1 1 -2 0 0 1 0 -1 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 4 -2 -3 -3 -3 -4 1 3 -3 -2 1 2 0 -2 6 1 3 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 4 -2 -2 -4 -3 -4 1 3 -3 -1 0 2 -1 -2 6 1 4 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -1 -2 -2 2 1 -2 -1 1 1 0 -1 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -1 4 1 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -1 -2 -3 2 1 -2 -1 2 1 0 -1 4 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -2 0 -1 -2 2 0 -1 0 2 0 0 0 2 -1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 -1 -1 -1 -1 1 0 -1 0 0 1 0 0 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -1 4 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -1 -2 -2 -3 1 2 -2 0 0 1 -1 -1 4 1 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 4 -2 -2 -4 -3 -4 1 3 -3 0 0 2 -1 -2 7 1 3 1 2
  3 0 3 -1 0 0 -1 -1 0 0 -4 -4 1 0 1 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -3 5 -1 2 -1 0 0 -2 -1 -3 -5 3 -4 1 -1 -1 5 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 0 0 0 -1 0 -1 -3 1 -2 0 -1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 3 -1 0 0 -1 -1 0 0 -3 -4 1 -1 1 -1 -1 3 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -2 4 -1 1 -1 0 0 -1 -1 -3 -4 2 -2 2 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 0 0 0 0 0 -2 -2 1 0 1 -1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 3 -2 0 -2 1 -1 0 1 1 -1 1 -1 3 0 -1 1 -1 -1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 0 1 1 -1 1 -1 2 1 0 0 -1 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 1 1 -1 -1 0 -1 -1 1 1 -3 -1 0 2 2 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 0 0 0 0 0 -2 -1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 2 -1 0 0 0 -1 0 1 -2 -2 0 0 1 0 -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 -2 5 -1 1 0 -1 -1 0 -1 -5 -5 2 -1 2 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -2 4 -1 1 0 -1 0 0 -1 -4 -4 2 -2 2 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -1 3 -1 0 0 -1 -1 1 0 -4 -3 1 0 2 -1 -1 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 3 -1 0 0 -1 -1 0 0 -3 -4 1 0 1 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 2 -1 -1 -1 1 0 0 1 1 -1 0 -1 2 1 -1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 -1 0 0 0 0 0 0 -2 -2 1 -1 2 -1 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 0 0 1 0 1 -1 1 1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  40 40
  -1 1 -2 0 -1 0 0 0 1 0 0 2 -1 2 0 0 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 1 0 1 -1 0 1 -1 -1 0 0 1 -2 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 -1 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -2 2 0 1 -1 0 0 -1 -1 -1 -2 1 -2 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 0 -1 0 0 -1 -2 -2 1 -1 0 -1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 -1 1 0 0 -1 0 -1 -2 -2 1 -1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 1 0 1 0 0 0 -1 -1 0 -1 1 -1 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -2 2 0 1 0 0 0 -1 -2 -1 -2 2 -2 -1 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 -1 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 1 0 1 -1 1 0 -1 -1 0 0 1 -2 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 1 0 1 0 0 0 -1 -1 0 -1 1 -1 -1 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -3 3 0 1 -1 0 0 -1 -1 -2 -2 2 -2 1 0 -1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 3 2 3 0 -2 2 0 0 -2 1 2 -5 -1 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 0 1 1 1 1 -1 0 -1 1 0 1 0 -2 -1 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 1 2 1 2 0 -1 1 0 0 -1 1 1 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 0 1 1 2 0 -1 0 0 0 -1 1 1 -2 -1 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 1 2 0 -1 1 0 0 -1 0 1 -3 0 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 2 0 1 1 -1 1 0 1 -1 0 1 -2 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 2 1 1 1 -2 1 0 1 -1 1 1 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 2 1 2 0 -2 1 1 0 -1 0 2 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 2 1 2 0 -2 2 1 0 -1 0 1 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 2 1 1 1 -2 0 0 1 -1 1 1 -2 -1 -1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 2 2 2 0 -2 2 0 0 -1 0 1 -4 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 1 1 1 0 -1 1 0 0 -1 1 0 -2 -1 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 3 2 2 0 -2 2 0 1 -2 1 1 -4 -1 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 1 0 1 -1 0 0 1 0 0 0 -1 -1 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 2 1 1 0 -1 1 0 1 -1 1 0 -2 -1 -1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 3 1 2 1 -2 1 0 1 -2 1 2 -4 -1 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 1 1 1 0 -1 1 1 0 -1 0 1 -2 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 2 2 3 0 -2 1 0 0 -1 1 1 -4 -1 -1 -1 -1
  40 40
  2 -1 3 -1 0 0 0 -1 0 0 -3 -3 1 -1 2 -1 -1 3 0 2 0 -3 1 1 2 2 2 0 -2 1 1 0 -1 1 1 -3 -1 -2 -1 0
  3 0 4 -1 0 1 -2 -1 1 -1 -5 -5 2 0 1 -2 -1 4 1 2 -1 1 0 -2 -1 -1 -2 0 1 -1 0 1 0 0 -1 3 0 1 1 1
  3 0 4 -1 0 1 -2 -1 0 -1 -5 -5 2 0 1 -2 0 4 2 1 0 0 0 0 0 0 0 -1 1 0 0 0 -1 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 0 1 -1 -3 -2 1 0 1 -1 -1 2 0 1 -2 2 0 -3 -2 -2 -4 1 2 -2 -1 2 1 0 -2 6 0 2 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -2 1 -1 2 1 0 1 -2 0 0 2 -1 1 1 -1 -1 -1 0 0
  1 1 0 -1 0 1 0 0 1 0 -2 -1 0 1 1 -1 0 1 -1 0 -1 0 0 -1 0 -1 -1 1 0 -1 0 1 0 0 0 2 -1 1 0 1
  1 0 1 0 0 1 -1 0 0 -1 -1 -1 1 0 0 -1 0 1 1 0 -1 1 0 -1 -1 -1 -2 0 2 -1 0 1 0 0 -1 3 0 1 0 1
  1 0 2 0 0 1 -1 0 0 -1 -2 -2 1 0 0 -1 0 2 1 0 0 0 0 0 -1 0 -1 -1 1 0 0 0 0 0 -1 1 0 1 0 1
  2 0 3 -1 0 0 -1 -1 0 -1 -3 -3 1 0 1 -1 0 3 1 1 0 0 0 -1 -1 0 -1 0 1 -1 -1 1 0 1 -1 1 0 1 0 1
  1 -1 2 -1 1 0 0 0 0 -1 -2 -2 1 -1 1 -1 0 3 0 1 0 -1 0 -1 0 0 -1 1 0 -1 -1 2 0 1 -1 1 -1 1 0 1
  3 0 4 -2 0 1 -1 -2 1 -1 -5 -5 1 0 2 -1 -1 4 1 2 1 -2 1 0 2 1 2 0 -1 1 0 0 -2 1 1 -3 -1 -1 -1 0
  2 -1 3 -1 1 0 0 0 -1 -1 -3 -4 2 -2 1 -2 0 4 1 2 0 -2 0 0 1 1 1 0 -1 0 0 1 -1 1 1 -1 -1 -1 0 0
  1 2 0 -1 -1 1 -1 -1 2 0 -2 -1 -1 2 1 -1 0 1 -1 0 0 0 0 -2 0 0 -1 1 0 -1 -1 2 0 1 -1 1 -1 1 0 1
  0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 2 1 1 0 -1 1 0 1 -2 1 1 -2 -1 -1 -1 0
  2 1 2 -1 0 1 -1 -1 1 0 -3 -3 0 1 1 -1 -1 2 0 1 -1 1 0 -2 -1 -1 -2 1 1 -1 0 1 0 0 -1 3 -1 2 0 1
  2 0 2 -1 0 1 -1 0 1 -1 -3 -3 1 0 1 -1 -1 3 0 1 -1 0 1 -2 0 -1 -2 1 0 0 0 2 0 0 -1 2 -1 1 0 1
  2 1 2 -1 0 1 -1 -1 1 0 -3 -3 0 1 1 -1 0 2 0 0 -1 2 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -2 4 0 3 0 2
  2 -1 3 -2 1 1 0 0 0 -2 -3 -4 2 -2 1 -1 -1 4 1 2 0 -1 1 -2 1 -1 -1 1 0 0 -1 2 -1 1 0 1 -1 0 0 1
  1 -1 2 0 1 0 0 0 -1 -1 -1 -2 1 -1 0 -1 0 2 1 1 0 -1 0 0 0 1 0 0 0 0 0 1 -1 1 0 0 -1 0 0 0
  1 -1 2 0 1 0 0 0 0 -1 -2 -2 1 -1 1 -1 0 2 0 1 0 0 -1 0 -1 0 0 0 0 -1 0 0 0 0 0 1 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 -1 -3 1 1 -1 0 1 1 0 -2 3 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -1 -1 -1 -2 1 1 -1 -1 1 1 -1 -1 2 0 1 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -1 -2 -2 -3 1 2 -2 -1 0 2 -1 -2 4 1 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 0 -2 -1 -1 0 1 -1 0 -1 1 -1 -1 2 1 1 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -1 -1 -1 -2 0 2 0 0 0 0 -1 -1 2 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -2 -1 -2 -3 1 2 -1 -1 1 1 0 -2 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 -1 0 1 0 0 0 0 -1 -1 1 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -3 -3 -4 0 3 -2 -1 0 2 0 -3 6 1 3 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 -2 -2 -3 0 2 -1 0 0 2 -1 -2 4 1 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -2 4 0 3 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -1 -2 0 1 0 1 0 1 -1 -1 2 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 -1 -1 -3 1 1 -1 0 1 1 -1 -1 3 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -3 -2 -4 1 2 -2 -1 1 2 -1 -2 5 0 3 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 -1 -2 1 1 -1 -1 1 1 0 -1 2 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -2 -1 -2 -3 1 2 -1 -1 1 0 0 -2 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 -2 -2 0 2 -1 0 0 0 0 -1 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 0 -2 -1 -1 0 2 -1 0 -1 1 -1 -1 2 0 2 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -1 -1 0 1 0 1 -1 1 -1 -1 2 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 1 1 0 -1 1 0 0 0 0 0 -2 0 -1 0 -1
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -2 3 -1 2 0 0 0 -1 -2 -2 -4 2 -3 0 -1 0 4 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 -1 4 -1 1 0 -1 -1 0 -1 -4 -5 2 -1 1 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 -1 0 1 0 0 1 -1 -1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 1 0 2 0 1 1 -1 -1 1 -1 1 -3 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 2 -2 0 -1 1 0 0 1 0 0 1 -1 2 -1 0 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 -1 0 0 0 0 1 0 -1 -1 0 0 1 0 -1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 -1 1 0 -3 -3 1 1 1 -1 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -2 3 -1 1 -1 0 -1 0 0 -3 -3 1 -1 2 0 -1 3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 0 0 -1 1 0 -2 -1 0 1 1 0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 0 3 -1 0 0 -1 -1 0 0 -4 -4 1 0 1 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 1 0 1 0 0 0 0 -1 -1 -1 1 -1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -2 3 -1 1 -1 0 0 -1 -1 -3 -3 2 -2 1 -1 0 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 0 1 0 -3 -3 1 0 1 -1 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 -1 1 -1 -3 -3 1 0 0 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 0 0 -1 0 0 -3 -3 1 0 1 -1 0 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 -1 1 -1 -3 -3 1 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 -1 0 0 0 0 0 1 1 0 1 -1 1 1 0 0 -1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 1 0 -1 0 1 0 0 1 0 -2 -1 0 1 1 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 1 2 -1 -1 1 0 -1 -1 0 1 -2 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 2 2 2 0 -2 2 1 0 -1 0 1 -3 -1 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 1 0 0 0 -1 1 1 0 0 0 0 0 0 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 2 2 2 0 -2 1 0 0 -1 1 1 -3 -1 -1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -2 5 0 3 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 2 1 1 2 0 -1 1 1 -1 0 -1 1 -2 0 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 4 -2 -2 -4 -3 -4 1 3 -3 -1 0 3 -1 -3 7 1 4 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 -1 -1 -1 -2 1 1 -2 -1 1 1 0 -1 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -1 -2 -3 1 2 -1 -1 1 1 0 -2 4 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 2 2 1 2 -1 -1 2 1 -1 -1 0 1 -3 0 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 3 2 3 0 -2 1 0 0 -2 1 2 -4 -1 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -2 -1 -1 -2 1 1 -1 -1 1 1 0 -1 3 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -2 0 -1 -2 1 1 -1 -1 2 0 1 -1 3 -1 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -1 -3 -2 -3 0 3 -2 -1 0 2 0 -3 5 1 3 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -2 -1 -2 -3 1 2 -1 -1 1 1 0 -2 4 0 2 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 -2 -2 1 1 -1 0 0 1 -1 -1 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 2 1 2 0 -2 2 1 0 -1 0 1 -3 -1 -1 -1 -1
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 0 0 0 0 0 -1 -2 1 -1 0 0 -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 -1 4 -1 1 0 -1 -1 0 -1 -4 -5 2 -1 1 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 0 0 0 0 -1 -1 -2 1 -1 0 0 -1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 1 -1 0 0 0 1 1 1 3 -1 2 0 1 0 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 0 0 -1 0 -1 -1 -2 1 -1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 -1 0 0 -1 -1 -1 -2 1 -1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 0 0 -1 0 -1 0 0 -1 -1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 0 0 0 -1 0 0 -1 -1 -1 1 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -2 1 1 1 -1 0 0 -1 -1 1 0 1 -2 -1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 -1 1 -1 -2 -3 1 0 0 0 -1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 1 0 1 0 0 0 0 -1 -1 -1 1 -1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 -1 1 0 0 1 -1 2 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 1 1 0 0 1 -1 -1 1 0 -1 -2 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 1 0 0 0 0 0 0 1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 0 0 0 -1 -1 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -2 2 0 1 0 0 0 0 -2 -1 -2 2 -2 0 0 -1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 1 0 0 0 0 0 0 2 2 -1 1 -2 1 1 -2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 -1 1 0 0 1 -1 1 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -2 -2 -2 -3 0 2 -2 -2 1 1 1 -2 4 1 2 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 0 -1 -1 -1 0 1 -1 0 0 1 0 -1 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 -1 -2 1 0 -1 0 1 1 0 -1 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 -1 -2 1 0 -1 0 1 1 0 -1 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 0 0 -1 1 -1 0 -1 0 0 0 1 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -1 -2 -2 -2 0 2 -2 0 -1 1 0 -1 4 1 2 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 -1 -2 0 1 -1 0 1 1 0 -1 3 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -2 -2 -3 0 2 -1 0 0 1 0 -2 4 1 2 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -1 -3 -3 -3 0 3 -2 0 -1 2 -1 -2 5 2 3 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -2 -1 -1 2 0 0 -1 0 0 -1 2 1 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 -2 -2 1 1 -1 0 1 1 0 -1 3 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 -1 -1 -1 0 1 -1 -1 0 1 0 -1 2 1 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1 0 0 0 0 0 -1 1 0 1 -1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -1 -2 -2 -3 1 2 -2 -1 0 2 0 -2 4 1 2 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 -1 -1 1 0 1 0 1 0 0 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -1 -2 -3 1 2 -1 0 1 0 0 -1 4 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 -2 -2 -3 0 2 -1 0 0 1 0 -2 4 1 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 -1 -1 -3 -2 -3 0 2 -2 0 0 2 0 -2 5 1 2 1 2
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 0 -1 0 -1 -1 1 0 -2 0 0 2 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 3 -1 0 0 -1 -1 0 -1 -3 -3 1 0 1 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 1 0 -1 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 1 0 0 0 0 0 0 -1 -1 -1 1 -1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 1 0 0 -1 0 0 -1 0 -1 -1 1 -1 1 -1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 0 0 -1 0 0 -1 -1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 -1 1 0 0 0 0 -1 -1 -2 1 -1 1 0 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 1 -1 0 0 0 0 0 -1 -1 -1 1 -1 1 0 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 -1 4 -1 0 0 -1 -1 0 -1 -4 -4 2 -1 1 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 1 -1 0 1 0 0 1 0 2 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 -1 1 1 0 1 -1 2 1 0 0 -1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -3 3 0 1 -1 0 0 -1 -1 -1 -2 2 -3 1 0 -1 3 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 0 0 -1 1 0 -1 -1 0 0 1 0 -1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 0 0 1 1 1 -1 1 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -3 -3 -4 0 3 -2 0 0 1 -1 -2 6 1 3 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 3 -1 -2 -2 -2 -3 1 2 -2 0 1 1 -1 -1 5 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 -1 -2 1 1 -1 0 1 0 0 -1 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 -1 -2 0 2 -1 0 1 0 0 -1 3 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -3 -1 -2 -3 1 1 -1 -1 2 0 0 -1 4 0 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -2 -1 -3 1 1 -2 -1 2 1 0 -2 4 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 -1 -1 1 0 -1 0 1 0 0 0 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 -1 1 0 -1 -1 2 0 1 -1 1 -1 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 1 0 -1 1 -1 0 0 2 -1 1 0 0 -1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -2 -2 -3 1 2 -2 -1 2 1 0 -2 5 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -2 -2 -3 1 1 -1 0 1 1 -1 -1 4 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -1 -1 0 1 0 1 0 0 -1 0 2 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -1 -2 -3 1 1 -1 0 1 0 0 -1 4 0 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 4 -1 -4 -3 -3 -6 2 3 -3 -2 3 2 0 -3 8 0 3 2 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -2 -2 -4 1 2 -2 -1 2 1 0 -2 5 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -2 -2 -3 0 2 -2 -1 1 1 0 -2 5 1 2 1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 1 0 0 -1 2 0 0 -1 1 -1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -3 -2 -2 -4 2 2 -2 -2 3 1 0 -2 5 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -3 -2 -3 -4 2 2 -2 -1 2 1 0 -2 5 0 3 0 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 -1 -1 -1 0 1 -1 1 0 0 -1 0 2 0 1 0 0
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 -1 0 1 -1 -1 1 -1 -3 -3 1 0 0 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 1 0 0 0 -1 -1 -2 1 -1 0 -1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 0 0 0 0 0 0 1 0 -1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 -1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 0 0 0 1 1 0 0 2 2 -1 0 -1 0 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 -1 0 1 0 0 -1 -1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 -1 1 0 0 -1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 1 0 1 0 0 0 -1 -1 1 -1 1 -2 -1 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 0 0 0 1 0 0 0 2 2 -1 0 -1 0 1 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 1 0 -1 0 1 0 0 1 0 -1 -1 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 -1 1 0 0 -1 0 -1 -1 -2 1 -1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 0 1 0 0 0 -1 1 0 0 0 -2 0 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 1 0 1 0 1 0 -1 -1 1 -1 1 -2 -1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 3 -3 0 -1 1 0 0 1 1 2 2 -2 2 -1 0 1 -2 -1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 0 1 0 0 0 0 -1 -1 -2 1 -2 0 -1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -2 -1 -2 -2 1 2 -1 -1 1 0 0 -1 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 1 0 -1 1 0 0 -1 0 1 -1 0 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 1 0 -1 1 1 0 -1 0 1 -1 0 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 2 2 1 3 -1 -1 2 1 -1 -2 0 2 -4 0 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 -1 -1 1 0 1 0 1 0 0 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 -1 2 1 1 1 -2 0 -1 2 -1 1 1 -2 -1 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 1 0 -1 1 0 0 0 0 1 -1 0 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 1 1 1 0 -1 1 0 1 -1 0 1 -2 -1 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 2 2 2 0 -2 1 0 1 -1 1 1 -3 -1 -2 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 3 2 2 4 -1 -2 2 1 -2 -1 0 2 -5 0 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 0 -1 1 0 0 -1 0 -1 0 1 1 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 1 2 0 -1 0 0 0 -1 0 1 -2 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -2 0 -2 -1 1 1 -1 -1 1 0 0 0 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 1 2 -1 -1 0 0 -1 0 0 1 -2 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 1 2 -1 -1 0 0 -1 0 0 1 -2 1 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 1 2 2 -1 -1 1 0 0 -1 1 1 -3 0 -2 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 2 1 3 2 2 0 -2 2 0 1 -2 1 1 -4 -1 -2 -1 -1
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 0 -1 0 0 0 0 0 1 0 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 -2 0 0 -1 1 0 0 0 2 2 -1 0 0 1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 0 -3 1 0 -1 1 1 -1 1 4 4 -1 0 -1 1 1 -3 -1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 0 -3 1 0 -1 1 1 0 1 4 4 -2 0 0 1 0 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 1 -1 1 0 -1 0 1 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 -1 0 -1 0 0 -1 -1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 -1 1 0 0 -1 0 -1 -1 -2 1 -1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 0 0 -1 1 0 -1 -1 0 0 1 0 -1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 -1 0 0 0 0 0 1 0 1 1 -1 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 -1 1 0 0 0 0 -1 -1 -2 1 -1 1 0 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 -1 1 0 -1 0 0 0 1 2 2 -1 1 0 1 0 -2 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 -1 0 0 -1 1 0 0 0 2 2 -1 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 0 0 0 -1 -1 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 0 -1 0 0 0 1 1 2 3 -2 2 0 1 0 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -2 -1 -2 -2 1 2 -1 -1 1 0 0 -1 3 0 2 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 1 1 1 0 -1 1 0 1 -1 0 1 -1 -1 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 1 1 1 0 -1 0 0 1 -1 1 1 -1 -1 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 3 1 2 1 -2 1 0 1 -2 1 2 -3 -1 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 2 0 1 1 -1 1 0 1 -1 0 1 -2 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 2 1 2 0 -1 1 1 0 -1 0 1 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 2 1 2 1 -2 1 1 0 -1 0 1 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 -1 -1 1 0 0 0 2 -1 0 0 1 -1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 2 1 2 0 -1 2 1 0 -2 0 1 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 1 1 1 0 -1 1 0 1 -1 1 0 -1 -1 -1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 -1 1 0 0 0 1 -1 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 2 1 1 0 -1 1 0 1 -2 0 1 -2 -1 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 -1 1 0 0 0 1 -1 0 0 1 -1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -2 0 -2 -1 1 1 -1 -1 1 0 0 0 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 2 1 1 0 -1 1 0 1 -1 1 0 -2 -1 -1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 2 1 1 0 -1 1 0 1 -2 1 1 -2 -1 -2 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 2 1 2 0 -1 1 1 0 -2 1 1 -3 -1 -1 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 1 1 2 0 -1 1 1 0 -1 0 1 -2 -1 -1 -1 -1
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 -1 0 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 1 1 0 -1 0 0 0 0 0 1 -2 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 -1 0 0 0 0 0 1 -2 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 2 0 2 2 -1 -1 0 1 -1 0 0 1 -2 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 2 1 1 -2 0 0 1 0 0 1 -2 -1 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 1 0 0 -1 0 0 0 0 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 1 2 0 -1 0 0 0 0 0 1 -2 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 -2 -1 -2 0 2 -1 0 0 1 -1 -1 3 1 1 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 1 1 0 -1 1 0 0 0 0 1 -2 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1 -1 1 0 0 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 3 2 3 1 -3 1 0 1 -1 1 2 -5 -1 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -1 -1 -3 1 1 -1 -1 2 1 0 -1 3 0 1 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 1 1 0 -1 0 0 0 0 0 1 -1 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 1 1 0 -1 0 0 0 0 0 1 -2 0 -1 0 0
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 0 0 0 0 1 0 1 -1 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 0 0 0 -1 0 0 -1 -2 -1 1 0 0 -1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 0 0 0 1 1 0 0 2 2 -1 0 -1 0 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 2 -1 0 -1 0 0 -1 1 1 0 1 -2 2 0 0 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 -1 0 0 -1 1 0 0 0 2 2 -1 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 -1 0 0 0 -1 1 -1 -2 -1 0 0 1 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 -1 -1 0 0 0 1 0 0 1 -1 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 3 -3 0 -1 1 0 0 1 1 2 2 -2 2 -1 0 1 -2 -1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 0 0 0 0 1 0 1 0 -1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 -1 0 -1 0 0 0 0 0 0 1 -1 1 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 3 -1 0 0 -1 -1 0 -1 -3 -3 1 0 1 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -2 0 0 0 1 0 0 0 2 2 -1 0 -1 0 1 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 2 -1 0 -1 1 -1 -1 1 0 0 1 -1 2 -1 0 1 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 -1 -2 1 1 -1 -1 1 1 0 -1 2 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 4 -1 -2 -3 -3 -4 1 3 -2 -1 1 2 -1 -2 6 1 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 -1 0 -1 0 1 0 0 0 1 0 -1 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 -1 -2 1 1 -1 -1 1 1 0 -1 2 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 -1 -1 0 1 -1 -1 0 1 0 -1 2 1 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 -1 -1 1 0 -1 0 1 0 -1 1 1 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 2 0 2 2 -1 -1 1 0 -1 0 0 1 -3 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 1 2 2 -1 -1 1 0 0 -1 1 1 -3 0 -2 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 1 2 0 -1 1 -1 0 0 0 1 -3 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 -1 -1 1 0 0 0 1 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1 0 -1 -1 1 0 0 0 1 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 1 2 1 2 0 -1 1 0 0 -1 1 1 -3 0 -2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 -1 -1 1 1 0 -1 1 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 2 1 1 0 -1 1 -1 1 -1 1 1 -3 0 -2 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 1 1 1 2 -1 -1 2 0 -1 -1 0 1 -3 0 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 -1 -1 0 1 0 -1 0 1 0 -1 1 1 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 -1 -1 1 1 1 -1 1 0 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 -1 0 -2 1 0 -1 -1 2 1 0 -1 2 0 0 1 0
  40 40
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -1 3 -1 1 0 0 0 0 -1 -3 -4 2 -2 1 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 1 1 0 -1 1 -1 -1 1 0 -2 -1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 1 0 0 0 -1 0 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -1 -2 -2 1 1 -1 -1 1 1 0 -1 3 0 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 -1 0 0 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 1 0 0 -1 1 0 0 0 0 -1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -2 -1 -1 -2 1 1 -1 -1 1 1 0 -1 3 0 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 -1 0 0 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 0 -1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 2 1 2 0 -1 1 0 0 -1 1 1 -3 -1 -1 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 -1 1 0 1 0 0 -1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 1 -1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 -1 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 -1 1 0 0 0 0 -1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 1 2 2 0 -1 1 0 0 -1 0 1 -3 -1 -1 0 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 -2 -1 -1 0 1 -1 0 -1 2 -1 -1 2 1 1 1 1
  
  

• PROPERTIES
  Unimodular=1
  

• REFERENCES
  G. Nebe, Finite quaternionic matrix groups.
  Represent. Theory 2 (1998) 106-223
  

• URL (links to other sites for this lattice)
  All the quaternionic matrix groups
  

• LAST_LINE
  
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe