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 = sys.stdin.buffer.readline

N = int(input())
A = list(map(int, input().split()))

sum_N = N * (N + 1) // 2
sum_A = sum(A)

if sum_A % sum_N != 0:
    print("NO")
    exit()
else:
    k = sum_A // sum_N

B = []
for i in range(N):
    if i + 1 != N:
        B.append(A[i + 1] - A[i] - k)
    else:
        B.append(A[0] - A[i] - k)

cnt = 0
for b in B:
    if b % N == 0 and b <= 0:
        k += b // N 
    else:
        print("NO")
        exit()

if k == 0:
    print("YES")
else:
    print("NO")