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 main():
    n = int(raw_input())
    a = map(int, raw_input().split())
    s = sum(a)
    t = n * (n + 1) / 2
    if s % t:
        print "NO"
        return
    t = s / t
    a += [a[0]]
    b = [a[i+1] - a[i] - t for i in xrange(n)]
    c = [0] * (n + n)
    d = [0] * (n + n)
    for i, x in enumerate(b):
        if x % n:
            print "NO"
            return
        b[i] = -x / n
        c[i+n] += b[i]
    b += [0] * n
    k = 0
    s = 0
    for i in xrange(n + n):
        k += b[i]
        d[i] += s if s > 0 else 0
        s += k
        k -= c[i]
        s -= c[i] * (n + 1)
    for i in xrange(n):
        if a[i] != d[i] + d[i+n]:
            print "NO"
            return
    print "YES"
main()
