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#! /usr/bin/perl -wl
use strict;
...

  return;
}

x11 x12 x13
x21 x22 x23
x31 x32 x33

S = 4*S - 3*S
  = (x21 + x22 + x23)
...
   -(x21 + x22 + x23)
   -(x31 + x32 + x33)
  = 3*x22

From choice of x, y, and z we have:
  x11 = x + y
...
     = 2x - 2y + z + x23
  So
    x23 = x + 2y - z

  x11 + x12 + x13
    = (x + y) + (x - z) + (x - y + z)
...
  x13 + x22 + x31
   = (x - y + z) + (x) + (x + y - z)
   = 3x