Divisible Subsequence

You are given a sequence of n integers. Your task is to determine whether there exists at least one non-empty subsequence whose sum is divisible by 13.

A subsequence is a sequence that can be derived from the original sequence by deleting some or no elements without changing the order of the remaining elements.

In mathematical terms, given a sequence \(a_1, a_2, \dots, a_n\), find if there exists a non-empty subset of indices \(I \subseteq \{1,2,\dots,n\}\) such that

\(\sum_{i \in I} a_i \equiv 0 \pmod{13}\)

If such a subsequence exists, print YES; otherwise, print NO.

inputFormat

The input is given via standard input and consists of two lines:

1. The first line contains a single integer n (\(1 \le n \le 10^5\)), which is the number of elements in the sequence.
2. The second line contains n space-separated integers \(a_1, a_2, \dots, a_n\) (\(|a_i| \le 10^9\)).

Note: In practice, given the constraints, an efficient algorithm (using dynamic programming with modulo arithmetic) is required to solve this problem.

outputFormat

Output a single line to standard output. The output should be YES if there exists at least one subsequence whose sum is divisible by 13, and NO otherwise.

## sample

5
1 2 3 4 5

YES

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