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: Wrong Answer)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet};

mod util {
    use std::io::stdin;
    use std::str::FromStr;
    use std::fmt::Debug;

    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn get<T: FromStr>() -> T
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    }

    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }

    #[allow(dead_code)]
    pub fn get2<T: FromStr, U: FromStr>() -> (T, U)
    where
        <T as FromStr>::Err: Debug,
        <U as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    }

    #[allow(dead_code)]
    pub fn get3<S: FromStr, T: FromStr, U: FromStr>() -> (S, T, U)
    where
        <S as FromStr>::Err: Debug,
        <T as FromStr>::Err: Debug,
        <U as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    }
}

#[allow(unused_macros)]
macro_rules! debug {
    ($x: expr) => {
        println!("{}: {:?}", stringify!($x), $x)
    }
}

fn main() {
    let n: usize = util::get();
    let mut a: Vec<i64> = util::gets();

    let total = a.iter().sum::<i64>();
    let add = (1..n + 1).sum::<usize>() as i64;

    if total % add != 0 {
        println!("NO");
        return;
    }

    let m = total / add;

    let a0 = a[0];
    a.push(a0);
    let v = a.windows(2)
        .map(|v| {
            let sub = v[1] - v[0];
            if (m - sub) % n as i64 == 0 {
                Some((m - sub) / n as i64)
            } else {
                None
            }
        })
        .collect::<Vec<_>>();

    if v.iter().all(|o| o.is_some()) && v.iter().map(|o| o.unwrap()).sum::<i64>() == m {
        let v = v.iter().map(|o| o.unwrap()).collect::<Vec<_>>();
        let mut b = Vec::new();
        let mut x = v.iter()
            .enumerate()
            .map(|(i, &a)| a * (n - i) as i64)
            .sum::<i64>();
        b.push(x);
        for i in 1..n {
            x -= v[i - 1] * (n - 1) as i64;
            x += m - v[i - 1];
            b.push(x);
        }
        if b.as_slice() == &a[..n] {
            println!("YES");
        } else {
            println!("NO");
        }
    } else {
        println!("NO");
    }
}