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)

use std::io::*;
use std::str::FromStr;

fn main() {
    let n: i64 = read();
    let a: Vec<i64> = (0..n).map(|_| read::<i64>()).collect();
    let sum: i64 = a.iter().sum();
    let mut ok = true;
    if (sum * 2) % (n * (n + 1)) == 0 {
        let k: i64 = (sum * 2) / (n * (n + 1));
        for i in 0..n as usize {
            if a[i] < k || k * n < a[i] {
                ok = false;
            }
            let d: i64 = a[((i + 1) as i64 % n) as usize] - a[i];
            if (d + k * (n - 1)) % n != 0 {
                ok = false;
            }
        }
    } else {
        ok = false;
    }
    println!("{}", if ok { "YES" } else { "NO" });
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}