Amy bought her $N$ friends each a gift, and wrapped them all. However, in her haste, she may have labelled them wrong! She labelled all of the gifts with integers $L_i$, but she may have made a mistake and forgotten a friend, or given one friend multiple gifts. Can you help her?

Constraints

$1\le L_i\le N\le {10}^6$

Subtask 1 [6/15]

$1\le N\le 2000$

Subtask 2 [9/15]

No additional constraints.

Input Specification

The first line will contain $N$, the number of friends Amy has.

The next line will contain $N$ space-separated integers $L_i$, the labels on the gifts.

Output Specification

If there are no duplicate labels and each friend from $1$ to $N$ received a gift, output YES.

Otherwise, output NO.

Sample Input 1

4
4 2 3 1

Sample Output 1

YES

Explanation for Sample Output 1

Each friend received a gift, and no friend received more than one gift, so Amy labelled her gifts correctly.

Sample Input 2

10
1 3 2 4 5 8 6 3 7 10

Sample Output 2

NO

Explanation for Sample Output 2

Note that friend number $9$ did not receive a gift.