# Is this a matrix or inequality?

Level pending

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 $$\mathfrak{C}$$.

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