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)

#!/usr/bin/env python3
if __name__ == '__main__':
  N = int(input())
  A = list(map(int, input().split()))

  q = (1+N)*N/2
  mi = 1000000009
  for i in range(0,N):
    mi = min(mi, A[i])
  p = mi//q
  for i in range(0,N):
    A[i] -= p * q

  ans = False
  while True:
    mi = 0
    ma = 0
    for i in range(0,N):
      if A[i] > A[ma]:
        ma = i
      if A[i] < A[mi]:
        mi = i

    if A[mi] < 0:
      ans = False
      break
    elif A[ma] == 0:
      ans = True
      break

    for i in range(0, N):
      A[(ma+1+i)%N] -= i+1

  # min(A) < 15
  if ans:
    print("YES")
  else:
    print("NO")

  # 1 2 3 4 5
  # 2 3 4 5 1
  # 3 4 5 1 2
  # 4 5 1 2 3
  # 5 1 2 3 4