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F. Permutation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a permutation of numbers from 1 to n. Determine whether there's a pair of integers a, b (1 ≤ a, b ≤ na ≠ b) such that the element (note, that it is usual division, not integer one) is between a and b in this permutation.

Input

First line consists of a single integer n (1 ≤ n ≤ 300000) — the size of permutation.

Second line contains n integers — the permutation itself.

Output

Print "YES", if such a pair exists, "NO" otherwise (in both cases without quotes, the answer is case insensitive).

Examples
Input
4
1 3 4 2
Output
NO
Input
5
1 5 2 4 3
Output
YES
Note

In the second example 2 is between 1 and 3. Additionally 4 is between 3 and 5.