Equal Sum Subarrays

FJ gave Bessie an array $a$ of length $N$ ($2\le N\le 500, -10^{15}\le a\_i\le 10^{15}$) with all $\frac{N(N+1)}{2}$ contiguous subarray sums distinct. For each index $i\in \[1,N]$, help Bessie compute the minimum amount it suffices to change $a\_i$ by so that there are two different contiguous subarrays of $a$ with equal sum.

The first line contains $N$.

The next line contains $a\_1,\dots, a\_N$ (the elements of $a$, in order).

One line for each index $i\in \[1,N]$.