Boxes

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

inputFormat

Input

The input is given from Standard Input in the following format:

N A_1 A_2 … A_N

outputFormat

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

样例

4
1 2 3 1

NO