B - Boxes

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

N 個の箱が円環状に並んでおり、i 番目の箱には A_i 個の石が入っています。

• 箱を一か所選ぶ。それを i 番目としたとき、1 から N の各 j に対して、i+j 番目の箱から石をちょうど j 個取り除く。
ただし、N+k 番目と表される箱は k 番目の箱と同一視するものとする。

### 制約

• 1 ≦ N ≦ 10^5
• 1 ≦ A_i ≦ 10^9

N
A_1 A_2A_N

5
4 5 1 2 3

YES

5
6 9 12 10 8

YES

4
1 2 3 1

### 出力例 3

NO

Score : 500 points

### 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.

### 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_2A_N

### Output

If it is possible to remove all the stones from the boxes, print YES. Otherwise, print NO.

5
4 5 1 2 3

### Sample Output 1

YES

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

5
6 9 12 10 8

YES

4
1 2 3 1

NO