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(a[0][0] + a[0][1]) (a[1][0] + a[1][1])
  (a[2][0] + a[2][1]) ... (a[N-1][0] + a[N-1][1])

$C[0] = 1;
$C[$N-1] = 1;
...
    $C[0] *= $a->[$i]->[0];
    $C[$N-1] *=  $a->[$i]->[1];
}

(a[0][0] + a[0][1]) * (a[1][0] + a[1][1]) =
 C[0] + C[1] + C[2] + C[3],
...
C[1] = a[0][0] * a[1][1]
C[2] = a[0][1] * a[1][0]
C[3] = a[0][1] * a[1][1]