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: Time Limit Exceeded)

use std::io::stdin;

#[allow(dead_code)]
fn input_ints() -> Vec<u64> {
    let mut st = String::new();
    match stdin().read_line(&mut st) {
        Ok(_) => st.split_whitespace().map(|s| s.parse().unwrap()).collect(),
        Err(_) => "".split_whitespace().map(|s| s.parse().unwrap()).collect(),
    }
}

fn take_stones(m: u32, v: &mut Vec<u64>) -> bool {
    let mut ans = true;
    let n = v.len() as u32;
    for i in 0..n {
        let ind = ((i + m) % n) as usize;
        if (i as u64) < v[ind] {
            v[ind] -= (i+1) as u64;
        } else {
            ans = false;
        }
    }
    ans
}

fn filled_or_not(n: u64, v: Vec<u64>) -> bool {
    let mut ans = true;
    for i in v {
        if n != i {
            ans = false;
        }
    }
    ans
}


#[allow(unused_variables)]
fn solve() {
    let n = input_ints()[0];
    let mut ns = input_ints();

    // let total: u64 = ns.iter().fold(1000000000, |m, i| if m + i);
    
    loop {
        let mut m: u64 = 1000000001;
        let mut index: u32 = 0;
        for i in 0..n {
            if m > ns[i as usize] {
                index = i as u32;
                m = ns[i as usize];
            }
        }

        if !take_stones(index, &mut ns) {
            break;
        }
    }

    let all0 = filled_or_not(0, ns);

    if all0 {
        println!("YES");
    } else {
        println!("NO");
    }
}

fn main() {
    solve();
}