Problem:
Score : 500 points

Problem Statement

There are N boxes arranged in a circle. The i-th box contains A_i stones.

Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:

Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.

Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.

Constraints

1 ≦ N ≦ 10^5

1 ≦ A_i ≦ 10^9

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N

Output

If it is possible to remove all the stones from the boxes, print YES. Otherwise, print NO.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>

int main(){
    int n;
    scanf("%d",&n);
    int a[n],i;
    long long int sum=0;
    for(i=1;i<=n;i++){
        scanf("%d",&a[i]);
        sum+=a[i];
    }
    long long int sigma=(n*(n+1))/2;
    if(sum%sigma!=0)printf("NO");
    else{
        
        while(a[1]>=1){
            int min=a[1],minnum=1;
            for(i=2;i<=n;i++){
                if(a[i]<min){
                    min=a[i];
                    minnum=i;
                }
            }
            //minとminの場所を求める
            int b[n];
            for(i=1;i<=minnum-1;i++)b[i]=a[i];
            for(i=minnum;i<=n;i++)a[i-minnum+1]=a[i];
            for(i=n-minnum+2;i<=n;i++)a[i]=b[i-n+minnum-1];
            //並び替え
            
            for(i=1;i<=n;i++)a[i]-=i;
            //引く
        }
        int flag=0;
        for(i=1;i<=n;i++)if(a[i]!=0)flag=1;
        if(flag==0)printf("YES");
        else printf("NO");
        
    }
    
    
    return 0;
}