Above shows a 6 by 6 square grid. Your objective is to place the numbers 1 to 6 such that each row and column contain each of the digits 1 to 6. The inequality constraints are specified between some of the squares to indicate one must be higher or lower than its neighbor. If \(A,B,C\) indicate the numbers in the square boxes as shown above, find the value of \(A\times B\times C\).

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