Problem Statement

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.

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.

Constraints

• 1 ≦ N ≦ 10^5
• 1 ≦ A_i ≦ 10^9

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

见题面 Input 部分

见题面 Output 部分