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
#!/usr/bin/env python3
import sys

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

S = N*(N+1) // 2
SA = sum(A)

if SA % S != 0:
    print("NO")
    sys.exit(0)

K = SA // S

# B = []
C = []
for i in range(N):
    # B.append(A[i] - A[i-1] - K)
    b = A[i] - A[i-1] - K
    if (b > 0) or (-b % N != 0):
        print("NO")
        sys.exit(0)
    C.append(-b//N)

print("YES")
