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
# -*- coding: utf-8 -*-

"""
解説PDFの英語版に従い実装
"""

import array
from bisect import *
from collections import *
import fractions
import heapq 
from itertools import *
import math
import random
import re
import string
import sys

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

A_sum = sum(A)
removed_unit = N * (N + 1) // 2

if A_sum % removed_unit:
    print('NO')
else:
    k = A_sum / removed_unit
    for i in range(N):
        d = A[(i + 1) % N] - A[i]
        if k - d >= 0 and (k - d) % N == 0:
            pass
        else:
            print('NO')
            sys.exit(0)
    print('YES')
