Score : $200$ points

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.

5
3 1 2 4 5

Yes

$(3, 1, 2, 4, 5)$ is a permutation of $(1, 2, 3, 4, 5)$, so we should print Yes.

6
3 1 4 1 5 2

No

$(3, 1, 4, 1, 5, 2)$ is not a permutation of $(1, 2, 3, 4, 5, 6)$, so we should print No.

3
1 2 3

Yes

1
1

Yes