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 Python (3.4.3) (judge verdict: Wrong Answer)

#import sys
#input = sys.stdin.readline
from itertools import accumulate
def main():
    N = int( input())
    A = list( map( int, input().split()))
    C = [0]*(N*2+2)
    L = [0]*(N*2+2)
    cnt = 0
    if sum(A)%(N*(N+1)//2) != 0:
        print("NO")
        return
    t = sum(A)//(N*(N+1)//2)
    for i in range(N):
        if (A[i] - A[i-1] + (N-1)*t)%N != 0:
            print("NO")
            return
        k =  (A[i] - A[i-1] + (N-1)*t)//N
        C[i] += t-k
        C[i+N] -= t-k
        cnt += t-k
        L[i+N] -= (t-k)*N
    S = list( accumulate(C))
    if cnt > t:
        print("NO")
        return
    for i in range(N*2+1):
        S[i+1] += S[i] + L[i+1]

    for i in range(N):
        if A[i] != S[i] + S[i+N]:
            print("NO")
            return
    print("YES")
    
            
if __name__ == '__main__':
    main()