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()))
d = [0] * N
for i in range(1, N):
  d[i] = a[i] - a[i - 1]
d[0] = a[0] - a[-1]
if sum(a) % (N * (N + 1) // 2):
  print("NO")
  exit(0)
f = 0
m = sum(a) // (N * (N + 1) // 2)
c = 0
for i in range(N):
  if m - d[i] < 0 or (m - d[i]) % N:
    f = 0
    break
  c += (m - d[i]) // N
  if c == m:
    f = 1
  else: f = 0
if c == 0:
  r = m
if c > m:
  l = m
if f:
  print("YES")
else: print("NO")