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
import sys

def solve():
    input = sys.stdin.readline
    N = int(input())
    A = [int(a) for a in input().split()]
    totalA = sum(A)
    if totalA % (N * (N + 1) // 2) != 0: print("NO")
    else:
        Op = totalA // (N * (N + 1) // 2)
        subA = [A[(i + 1) % N] - A[i] for i in range(N)]
        count = 0
        for i, a in enumerate(subA):
            if (Op - a) % N != 0 or a > Op:
                print("NO")
                break
            else: count += (Op - a) // N
        else: 
            if count == Op: print("YES")
            else: print("NO")
    
    return 0

if __name__ == "__main__":
    solve()

