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 $(1, 2, \dots, N)$.

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.

Constraints

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

Sample Input 1

5
3 1 2 4 5

Sample Output 1

Yes

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

Sample Input 2

6
3 1 4 1 5 2

Sample Output 2

No

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

Sample Input 3

3
1 2 3

Sample Output 3

Yes

Sample Input 4

1
1

Sample Output 4

Yes

见题面 Input 部分

见题面 Output 部分