Is this a matrix or inequality?

Given the $50 \times 50$ array $(a_{ij})_{ij}$ with $a_{ij} = i+j-1$ , let the smallest product of the $50$ elements of the array, under the condition that no two lie on the same row or column, be $\mathfrak{C}$ .

Evaluate $v_5(\mathfrak{C})$ , which basically means the exponent of $5$ in the factorisation of $\mathfrak{C}$ .