Dividing Stamps

Problem Code: DIVIDING Solved Submit

Problem Statement :

Are you fond of collecting some kind of stuff? Mike is crazy about collecting stamps. He is an active member of Stamp Collecting Сommunity(SCC).

SCC consists of N members which are fond of philately. A few days ago Mike argued with the others from SCC. Mike told them that all stamps of the members could be divided in such a way that i'th member would get i postage stamps. Now Mike wants to know if he was right. The next SCC meeting is tomorrow. Mike still has no answer.

So, help Mike! There are N members in the SCC, i'th member has Ci stamps in his collection. Your task is to determine if it is possible to redistribute C1 + C2 + ... + Cn stamps among the members of SCC thus that i'th member would get i stamps.

Input

The first line contains one integer N, denoting the number of members of SCC.

The second line contains N integers Ci, denoting the numbers of the stamps in the collection of i'th member.

Output

The first line should contain YES, if we can obtain the required division, otherwise NO.

Constraints

1 ≤ N ≤ 100 000;

1 ≤ Ci ≤ 10^9.

Examples

Input:

5

7 4 1 1 2

Output:

YES

Input:

5

1 1 1 1 1

Output:

NO