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::{self, Stdin};
use std::str::{self, FromStr};
use std::error::Error;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.ne();
    let mut a = vec![0i64; n];
    for x in &mut a {
        *x = sc.ne();
    }
    let sum: i64 = a.iter().fold(0, |acc, &x| acc + x);
    let sumn = {
        let mut r = 0i64;
        for i in 0..n {
            r += i as i64 + 1;
        }
        r
    };
    let mut ok = true;
    if sum % sumn != 0 {
        ok = false;
    }
    let key = sum / sumn;
    let mut cntd = 0;
    for i in 0..n {
        let j = (i + 1) % n;
        let x = a[j] - a[i];
        match x {
            val if val == key => {}
            val if val > 0 => ok = false,
            _ => {
                let d = key - x;
                if d % n as i64 != 0 {
                    ok = false;
                } else {
                    cntd += d / n as i64;
                }
            }
        }
    }
    if cntd != key {
        ok = false;
    }
    println!("{}",
             match ok {
                 true => "YES",
                 _ => "NO",
             });
}
struct Scanner {
    stdin: Stdin,
    id: usize,
    buf: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner {
            stdin: io::stdin(),
            id: 0,
            buf: Vec::new(),
        }
    }
    fn next_line(&mut self) -> Option<String> {
        let mut res = String::new();
        match self.stdin.read_line(&mut res) {
            Ok(0) => return None,
            Ok(_) => Some(res),
            Err(why) => panic!("error in read_line: {}", why.description()),
        }
    }
    fn next<T: FromStr>(&mut self) -> Option<T> {
        while self.buf.len() == 0 {
            self.buf = match self.next_line() {
                Some(r) => {
                    self.id = 0;
                    r.trim().as_bytes().to_owned()
                }
                None => return None,
            };
        }
        let l = self.id;
        assert!(self.buf[l] != b' ');
        let n = self.buf.len();
        let mut r = l;
        while r < n && self.buf[r] != b' ' {
            r += 1;
        }
        let res = match str::from_utf8(&self.buf[l..r]).ok().unwrap().parse::<T>() {
            Ok(s) => Some(s),
            Err(_) => panic!("parse error"),
        };
        while r < n && self.buf[r] == b' ' {
            r += 1;
        }
        if r == n {
            self.buf.clear();
        } else {
            self.id = r;
        }
        res
    }
    fn ne<T: FromStr>(&mut self) -> T {
        self.next::<T>().unwrap()
    }
}