# 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 \( \mathfrak{C} \).