

4 5
0 1 1 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

4 5
0 1 0 0 1
1 0 0 0 0
0 0 0 1 0
0 0 0 0 1


#5 5
#0 0 1 0 0
#0 1 1 0 0
#1 0 0 0 0
#0 0 0 1 0
#0 0 0 0 1
 7 6
   1    1   -1    0    1    0
   1   -1    1    0    0   -1
   1    0    0   -1    1    0
   1   -1    0    0    2    0
   1    1    0    0    0   -1
   1    0    0    1    0   -1
   1    0    0    0    0    1

#1 1 0 0 0 -1
#1 -1 0 0 2 0
#1 0 1 0 0 -1
#1 0 -1 0 1 0
#1 0 0 1 0 -1
#1 0 0 -1 1 0

1 3
1 1 -2



##### test

9 8
#  #   i    j    k   i0 j0 N    -
 	0   0    1    1   -1 0  0    0
	0   0    0    1   0 -1  0    0
   1   1   -1    0   0  0  1    0
   1  -1    1    0   0  0  0   -1
   1   0    0   -1   0  0  1    0
   1  -1    0    0   0  0  2    0
   1   1    0    0   0  0  0   -1
   1   0    0    1   0  0  0   -1
   1   0    0    0   0  0  0    1

# image par (i,j,k) -> (j+k,k)
6 7
0 1 1 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1
#
8 8
#  #   i    j    k   i0 j0 N    -
   1   -1   0    0    1 -1 -1  -1  # i = i0-j0-N
#	1   0   -1    0   1  -1  0  -1  # j = i0-j0
#	1   0    0   -1   0   1  0   0    #  j0 >= k
#	1   0    0    0   1   0  0   -3   # i0 >= 3
#	1   0    0    0   -1  0  2    -1   # i0 <= 2N-1
#	1   0    0    0   0   1  0   -1   # j0 >= 1
#	1   0    0    0   0  -1  1    0   # j0 <= N
   1   1   -1    0   0  0  1    0
   1   0    1    0   0  0 -1   -2
   1   0    0   -1   0  0  1    0
   1  -1    0    0   0  0  2    0
   1   1    0    0   0  0  0   -1
   1   0    0    1   0  0  0   -1
   1   0    0    0   0  0  0    1
0 5
i0 j0 N



# T P2 =
6 7
1    1   -1    0    0    0   -2
1   -1    1    1   -1    0   -1
1    0   -1    0    0    1    0
1   -1    1    0    0    1    1
1    0    1    0    0    0   -1
1    0    0    0    0    0    1

# T P3
7 7
   0    1   -1   -1    1    0    0
   1    0    0    1   -1    0   -2
   1    0   -1    0    1    0    0
   1    0   -1    0    0    1    0
   1    0    0   -1    1    1    1
   1    0    1    0    0    0   -1
   1    0    0    0    0    0    1



#########################
# T P1
6 7
   1    0   -1    0    0    1    0
   1    0    1    0    0    0   -1
   1    1   -1    0    0   -1   -2
   1   -1    1    0    0    3    0
   1   -1    1    1   -1    0   -1
   1    0    0    0    0    0    1

# T P2
6 7
   1    0    0   -1    1    3    0
   1   -1    1    1   -1    0   -1
   1    1   -1    0    0   -1   -2
   1    0    1    0    0    0   -1
   1    0   -1    0    0    1    0
   1    0    0    0    0    0    1

# T P3
7 7
   0    1   -1   -1    1    0    0
   1    0    0    1   -1   -1   -2
   1    0   -1    0    1    0    0
   1    0   -1    0    0    1    0
   1    0    0   -1    1    3    0
   1    0    1    0    0    0   -1
   1    0    0    0    0    0    1


### T (P1 U P2 U P3) =

6 7
   1    0   -1    0    0    1    0
   1    0    1    0    0    0   -1
   1    1   -1    0    0   -1   -2
   1   -1    1    0    0    3    0
   1    0    0    1   -1   -3   -1
   1    0    0    0    0    0    1
# => 0

6 7
   1    0   -1    0    0    1    0
   1    0    0   -1    1    3    0
   1   -1    1    1   -1    0   -1
   1    1   -1    0    0   -1   -2
   1    0    1    0    0    0   -1
   1    0    0    0    0    0    1
# =>  N (i0 - j0) - n - 2 N

7 7
   0    1   -1   -1    1    0    0
   1    0    0    1   -1   -1   -2
   1    0   -1    0    1    0    0
   1    0   -1    0    0    1    0
   1    0    0   -1    1    3    0
   1    0    1    0    0    0   -1
   1    0    0    0    0    0    1
# => j0



#############################################################"
# EP b
#
10 7
#  #   i    j       i0 j0 N    -
   0  -1    0       0   1  0   0  # i = j0 ( i <= j0 - 1 )
	1   0   -1       1   0  0  -1  # j <= i0 - 1

   1   1   -1       0  0  1    0
   1  -1    1       0  0  0   -1
   1  -1    0       0  0  2    0
   1   1    0       0  0 -1   -1

   1   0    0       -1  1  1    1
   1   0    0       1  -1  0   -2
   1   0    0       0  -1  2    0
   1   0    0       0   1 -1   -1

0 5
i0 j0 N


# P1 (i = j0, j <= i0 - 1)
 => i0 - j0 - 1

# P2 (i <= j0 - 1)
 => j0 N - N - N


