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: Accepted)

import os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7

N = int(sys.stdin.readline())
A = list(map(int, sys.stdin.readline().split()))


def solve(A):
    if N == 1:
        return True

    S = sum(A)
    if S % ((N + 1) * N // 2) != 0:
        return False
    # 箱を選ぶ回数
    K = S // ((N + 1) * N // 2)

    cnt = 0
    for i in range(N):
        j = (i + 1) % N
        d = A[j] - A[i]
        if (K - d) % N != 0:
            return False
        if (K - d) // N < 0:
            return False
        cnt += (K - d) // N
    return cnt == K


if solve(A):
    print('YES')
else:
    print('NO')