# Integer Array With Avoidance

Consider a $$100 \times 100$$ table, filled with integer entries from 1 to $$N$$ inclusive. The entry in the $$i$$th row and $$j$$th column is denoted by $$a_{i,j}$$. For all integers $$i$$ and $$j$$ such that $$i + j \leq 100$$, the integer $$a_{i,j}$$ does not appear in the $$(i+j)$$th row. What is the minimum value of $$N$$?

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