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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
  let n: i64 = read();
  let mut vec: Vec<i64> = read_vec();
  
  let sum = vec.iter().sum::<i64>();
  let psum = n * (n + 1) / 2;
  let k = sum / psum;
  if sum % psum != 0 {
    println!("NO");
    return
  };
  
  let &head = vec.first().unwrap();
  vec.push(head);
  
  if vec.windows(2).map(|w|w[1]-w[0]-k).all(|x|x<=0 && x%n==0) {
    println!("YES");
  } else {
    println!("NO");
  }
}

fn read<T: std::str::FromStr>() -> T {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().parse::<T>().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
}