Given an array A of N integers, find if there exists an index i and j (1 \le i, j \le N) such that the sum of the first i elements (prefix) is equal to the sum of the last j elements (suffix).
Note: The prefix and suffix can't overlap.
Input
The first line contains an integer N (1 \le N \le 10^5).
The second line contains N integers A_1, A_2, \dots, A_N (|A_i| \le 10^9).
Output
Print "YES" if such a prefix and suffix exist, and "NO" otherwise.
Examples
| standard input | standard output |
|---|
| 4
1 2 3 3
| YES
|
| 3
1 2 4
| NO
|