Dividing Stamps

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 C_i stamps in his collection. Your task is to determine if it is possible to redistribute C₁ + C₂ + ... + C_n 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 C_i, 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 ≤ C_i ≤ 10⁹.

Examples

Input:
5
7 4 1 1 2

Output:
YES

Input:
5
1 1 1 1 1

Output:
NO

Problem Link : DIVIDING

The idea :

The idea is that the sum of all elements should be equal to sum of all numbers from 1 to N. 

The Code :

#include <bits/stdc++.h>
#include <iostream>
using namespace std;
int main()
{
        int n,i;
        long int sum=0,c;
        scanf("%d",&n);
        for(i=0;i<n;i++)
        {
            scanf("%ld",&c);
            sum+=c;
        }
        if(sum==(n*(n+1))/2)
            printf("YES\n");
        else
            printf("NO\n");
    return 0;
}