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
def s(n,a):
    N=n*(n+1)/2
    sa=sum(a)
    if sa%N!=0:
        return False
    if sa<N:
        return False
    sn=sa/N
    da=[]
    for i in xrange(n-1):
        da.append(a[i+1]-a[i])
    da.append(a[0]-a[n-1])
    if max(da)>sn:
        return False
    if sum(da)!=0:
        return False
    for di in da:
        if (sn-di)%n!=0:
            return False
    return True
    
n = int(raw_input())
a = [int(i) for i in raw_input().split(" ")]
if s(n,a):
    print "YES"
else:
    print "NO"