Problem:
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_2 … A_N

Output

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

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

Solution in Python (3.4.3) (judge verdict: Wrong Answer)


def solve():
    n = int(input())
    a = list(map(int, input().split()))

    one = n*(n+1)/2

    if sum(a) % one != 0:
        print("NO")
        return
    else:
        nop = sum(a) / one

    d = [0 for i in range(n)]
    for i in range(n):
        d[i] = a[(i+1)%n] - a[i]
        d[i] = d[i] - nop

    count = 0

    for i in range(n):
        if d[i] != 0:
            if d[i] % n != 0:
                print("NO")
                return
            count = count + (-1*d[i]) / n
            d[i] = 0
            if count > nop:
                print("NO")
                return

    if sum(d) == 0 and count == nop:
        print("YES")
    else:
        print("NO")

solve()