FJ gave Bessie an array $a$ of length $N$ $(2 \leq N \leq 500, -10^{15} \leq a_i \leq 10^{15})$ 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 $a_1, \ldots, a_N$ (the elements of $a$, in order).

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

**For Example #1:** Decreasing $a_1$ by $2$ would result in $a_1+a_2=a_2$. Similarly, increasing $a_2$ by $3$ would result in $a_1+a_2=a_1$. **For Example #2:** Increasing $a_1$ or decreasing $a_3$ by $1$ would result in $a_1=a_3$. Increasing $a_2$ by $6$ would result in $a_1=a_1+a_2+a_3$.