#115Easy

Is it a permutation

Time: 1 s · Memory: 256 MB

Maps and sets

Statement

You are given an array of $n$ numbers. Is it a permutation of the numbers $1$ to $n$ , i.e. does each of $1, 2, \ldots, n$ occur exactly once (in any order)?

Input format

The first line contains $n$ ( $1 \le n \le 10^5$ ). The second line contains $n$ integers ( $∣ a_{i} ∣ \leq 10^{}$ ).

Output format

YES if it is a permutation, NO otherwise.

Examples

Input

6
5 2 1 4 3 6

Output

YES

Input

3
1 2 2

Output

NO

Note

Two conditions: every number is within $1 \le a_i \le n$ and none repeats. A set or a "seen" array of length $n + 1$ is enough. In the second example $2$ repeats and is missing — .