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,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time

sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7

def LI(): return list(map(int, input().split()))
def II(): return int(input())
def LS(): return input().split()
def S(): return input()

def main():
    n = II()
    a = LI()
    nn = n*(n+1)//2
    s = sum(a)
    if s%nn != 0:
        return "NO"
    k = s//nn
    km = k%n
    c = 0
    for i in range(n):
        t = a[i]-a[i-1]
        if t % n != km:
            return "NO"
        if t > k:
            return "NO"
        kt = k-t
        if kt%n != 0:
            return "NO"
        c += kt//n
    if c == k:
        return "YES"
    return 'NO'


print(main())
