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

b = [] #差
for i in range(1,n):
    b.append(a[i]-a[i-1])
b.append(a[0]-a[n-1])

w = n*(n+1)//2 #一回の操作で取り除く石の数


if sum(a)%w != 0:
    print('NO')
else:
    res = 0
    c = sum(a)//w #操作回数
    for i in range(n):
        b[i]-=c
    
    for i in range(n):
        if (-b[i]) % n == 0 and b[i] <= 0:
            res += (-b[i])//n
        else:
            res = c+1
            break
            
    if res == c:
        print('YES')
    else:

        print('NO')