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 (2.7.6) (judge verdict: Wrong Answer)

import numpy as np

N = int(raw_input())
n = np.array(map(int, raw_input().split()))

Nsum = np.sum(n)

if Nsum % np.sum(np.arange(N+1)[1:]):
    print 'NO'
    exit()
sa = np.append(n[1:], n[0]) - n

tmp = np.sum(sa % N != (Nsum / np.sum(np.arange(N+1)[1:]))%N)
tmp2 = np.sum(np.abs(sa) / N > (N-1)*Nsum / np.sum(np.arange(N+1)[1:]))
if tmp + tmp2:
    print 'NO'
else:
    print 'YES'