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 math
#import numpy as np
import queue
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)

def main():
    n = int(ipt())
    a = [int(i) for i in ipt().split()]
    sa = sum(a)
    if sa%(n*(n+1)//2) != 0:
        print("NO")
        exit()
    t = sa//(n*(n+1)//2)
    d = [a[i]-a[i-1] for i in range(n)]
    at = 0
    for i in d:
        if (t-i)%n != 0 or (t-i)//n < 0:
            print("NO")
            exit()
        at += (t-i)//n
    if at == t:
        print("YES")
    else:
        print("NO")

    return

if __name__ == '__main__':
    main()
