Equal Coin Split

You are given a collection of coins with positive integer values. The coins are arranged in a row. Your task is to determine whether it is possible to split the collection into two non-empty contiguous parts such that the sum of the coin values in the first part equals the sum of the coin values in the second part.

If a valid split exists, output YES x where x is the number of coins in the first part. Otherwise, output NO.

Note that the split must divide the list into two consecutive segments. The input starts with an integer n representing the number of coins, followed by n positive integers that denote the coin values. The solution should work for both small and large arrays efficiently.

Mathematically, let \(a_1, a_2, \ldots, a_n\) be the coin values. You need to find an index \(i\) (with \(1 \le i < n\)) such that:

[ \sum_{j=1}^{i} a_j = \sum_{j=i+1}^{n} a_j ]

If such an index exists, output YES i (using 1-indexing for the first part length); otherwise output NO.

inputFormat

The first line of input contains an integer n (1 ≤ n ≤ 10⁵), representing the number of coins. The second line contains n space-separated positive integers representing the values of the coins.

outputFormat

Output a single line. If there is a valid split, output YES x where x is the number of coins in the first part; otherwise, output NO.

## sample

6
1 2 3 3 2 1

YES 3

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