Find the Balance Point in an Array

You are given a list of integers. Your task is to find the balance point in the list.

A balance point is an index i such that the sum of all elements to the left of i is equal to the sum of all elements to its right. Formally, find an index i (0-indexed) such that

\(\sum_{j=0}^{i-1} a_j = \sum_{j=i+1}^{n-1} a_j\)

If such an index exists, output it. Otherwise, output \(-1\). Note that if the list is empty, the answer is \(-1\), and if the list contains a single element, the answer is \(0\) since the sums on both sides are \(0\).

inputFormat

The first line of the input contains a single integer \(n\) representing the number of elements in the list.

If \(n > 0\), the second line contains \(n\) space-separated integers representing the list.

outputFormat

Output a single integer representing the balance point index. If no balance point exists, output \(-1\).

## sample

7
1 2 3 4 3 2 1

3

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