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: Time Limit Exceeded)

#include <stdio.h>

int main(){
  int i,n, a[100000], count = 0,max = 1, i_max;

  scanf("%d", &n);
  for(int i = 0; i<n; i++){
    scanf("%d", &(a[i]) );
    if(a[i] > max){
      max = a[i];//最大値a[i]
      i_max = i;//最大値a[i]をとるi
    }
  }

  while(1){
      max = 0;
      i = i_max;

  for(int j = 0; j < n; j++){
    if(i < j){
      a[i - j + n] -= (n-j);
      // printf("a[%d] = %d\n", i-j+n, a[i-j+n]);
      if(a[i - j + n] > max){
        max = a[i - j + n];
        // printf("max is a[%d] = %d\n", i-j+n ,max);
        i_max = i - j + n;
      }else if(a[i - j+ n] == 0){
        count += 1;
        // printf("count = %d\n", count);
      }
    }else{
      a[i - j] -= (n-j);
      // printf("a[%d] = %d\n", i-j, a[i-j]);
      if(a[i - j] > max){
        max = a[i - j];
        // printf("max is a[%d] = %d\n", i-j ,max);
        i_max = i - j;
      }else if(a[i - j] == 0){
        count += 1;
        // printf("count = %d\n", count);
      }
    }
  }

  // printf("count = %d\n", count);
  if(count > 0){
    break;
  }
  }

  if(count == n){
    printf("YES\n");
  }else{
    printf("NO\n");
  }

  return 0;
}