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)

def main():
    n = int(input())
    a = list(map(int, input().split()))
    nn = (n*(n+1))//2
    sum_ = sum(a)
    a += [a[0]]
    cnt = sum_//nn
    if sum_ % nn != 0:
        print("NO")
        return 0
    ans = 0
    for i in range(n):
        p = a[i]-a[i+1]+cnt
        if p % n != 0:
            print("NO")
            return 0
        ans += p//n
    if ans == cnt:
        print("YES")
    else:
        print("NO")


main()