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
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n = int(input())
a = list(map(int, input().split()))

unit = n*(n+1)//2
k, m = divmod(sum(a), unit)
if m:
    ans = "NO"
else:
    count = [None] * n # iを選んだ回数
    for i in range(n):
        diff = a[i] - a[i-1]
        x, m = divmod(k- diff, n)
        if x<0 or m:
            ans = "NO"
            break
        count[i-1] = x
    else:
        if sum(count)==k and sum(c*(n-i) for i,c in enumerate(count)):
            ans = "YES"
        else:
            ans = "NO"
print(ans)