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 = input()
A = map(int, raw_input().split())
S = sum(A)
if S%(N*(N+1)/2)==0:
    c = S/(N*(N+1)/2)
    for i in range(N):
        A[i] -= c*(i+1)
    ans = "YES"
    for i in range(N-1):
        t = A[i]-A[(i+1)%N]
        if t<0 or t%N!=0:
            ans = "NO"
    print ans
else:
    print "NO"