题目描述

Note: The time limit for this problem is 3s, 1.5x the default.

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

输入格式

The first line contains $N$.

The next line contains $a_1, \cdots ,a_N$ (the elements of $a$, in order).

输出格式

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

样例 #1

样例输入 #1

2
2 -3

样例输出 #1

2
3

样例 #2

样例输入 #2

3
3 -10 4

样例输出 #2

1
6
1

提示

Explanation for Sample 1

Decreasing $a_1$ by $2$ would result in $a_1+a_2=a_2$. Similarly, increasing $a_2$ by $3$ would result in $a_1+a_2=a_1$.

Explanation for Sample 2

Increasing a1 or decreasing $a_3$ by $1$ would result in $a_1=a_3$. Increasing $a_2$ by $6$ would result in $a_1=a_1+a_2+a_3$.

SCORING

• Input $3$: $N \le 40$
• Input $4$: $N \le 80$
• Inputs $5-7$: $N \le 200$
• Inputs 8-16: No additional constraints.