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::stdin;

fn read_line() -> Vec<String> {
    let mut line = String::new();
    stdin().read_line(&mut line).expect("Failed to read line");
    return line.trim().split_whitespace().map(|s| s.to_string()).collect();
}

struct Reader {
    v: Vec<String>,
    n: usize,
}

impl Reader {
    fn new() -> Reader {
        let v = read_line();
        return Reader { v: v, n: 0 };
    }
    fn next<T>(&mut self) -> T where T: std::str::FromStr, T::Err: std::fmt::Debug {
        if self.n == self.v.len() {
            self.v = read_line();
            self.n = 0;
        }
        let x = self.v[self.n].parse().expect(&self.v[self.n]);
        self.n += 1;
        return x;
    }
    fn nexts<T>(&mut self, n: usize) -> Vec<T>
    where T: std::str::FromStr, T::Err: std::fmt::Debug {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            v.push(self.next());
        }
        return v;
    }
}

fn main() {
    let mut r = Reader::new();
    let n: usize = r.next();
    let a: Vec<usize> = r.nexts(n);

    let sum_a: usize = a.iter().sum();
    let sum_i = n * (n+1) / 2;
    if sum_a % sum_i > 0 {
        println!("NO");
        return;
    }
    let k = sum_a / sum_i;

    if (0..n).all(|i| (a[i]+k-a[(i+1)%n])%n == 0) {
        println!("YES");
    } else {
        println!("NO");
    }
}