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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
input = sys.stdin.readline

def main():
  n = int(input())
  alist = list(map(int, input().split()))
  asum = sum(alist)
  rm = (1 + n) * n // 2
  if asum % rm != 0:
    print('NO')
  else:
    k = asum // rm
    d = [a-pa-k for pa, a in zip(alist, alist[1:])]
    d.append(alist[0] - alist[-1] - k)
    nk = 0
    for _d in d:
      if _d % n != 0:
        break
      else:
        nk += abs(_d) // n
    else:
      if nk == k:
        print('YES')
      else:
        print('NO')
      sys.exit(0)
    print('NO')


if __name__ == '__main__':
  main()