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`.

Examples

Input

5
4 5 1 2 3


Output

YES


Input

5
6 9 12 10 8


Output

YES


Input

4
1 2 3 1


Output

NO
#!/usr/bin/env python
# -*- coding: utf-8 -*-

N = int(input())
A = list(map(int,input().split()))

def solve(A):
    n = sum(A) // (N*(N+1)//2)
    if sum(A) % (N*(N+1)//2) != 0:
        return 'NO'

    count = 0

    for i in range(N):
        diff = A[i] - A[i-1] 

        if diff == n:
            continue

        if -1 * (diff - n) % N != 0:
            return 'NO'
        c = -(diff-n)//N
        if c < 0:
            return 'NO'

        count += c

    if count == n:
        return 'YES'
    return 'NO'

print(solve(A))
        
