P12605 A. Prefixsuffix Sums

You are given an integer sequence $a$ of length $n$. You can perform the following operations any number of times (possibly, zero): Select indices $1 \le i, j \le n$ such that $i \ne j$, and perform the operation: $a_i \leftarrow a_i + 1$, $a_j \leftarrow a_j - 1$ simultaneously. Your task is to compute the minimum number of operations needed to make the sum of the prefix sums of $a$ equal to the sum of the suffix sums of $a$. That is, let $s_i=a_1+a_2+\dots+a_i,t_i=a_i+a_{i+1}+\dots+a_n$, you need to make $s_1+s_2+\dots+s_n$ equal to $t_1+t_2+\dots+t_n$. Note that $a_i$ can become negative after several operations.

The first line contains a single integer $n$. The second line contains $n$ integers $a_1,a_2,\dots,a_n$.

Print a single integer — the minimum number of operations needed. If it is impossible to satisfy the condition within $10^{100}$ operations, print $-1$.

This problem has subtasks. - Subtask 1 (30 points): $1 \le n \le 2$ - Subtask 2 (30 points): $a_i = i$ - Subtask 3 (5 points): $a_i = 1$ - Subtask 4 (35 points): No additional constraints It is guaranteed that for all testcases, $1 \le n,a_i \le 10^6$.