Problem Statement

You are given a sequence of $N$ integers between $1$ and $N$ (inclusive): $A = (A_1, A_2, \dots, A_N)$.

Determine whether $A$ is a permutation of $(1, 2, \dots, N)$.

Constraints

• $1 \leq N \leq 10^3$
• $1 \leq A_i \leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

If $A$ is a permutation of $(1, 2, \dots, N)$, print Yes; otherwise, print No.