Problem:
Score: 300 points

Problem Statement

We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.

Determine if he is correct.

Constraints

c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive).

Input

Input is given from Standard Input in the following format:

c_{1,1} c_{1,2} c_{1,3}
c_{2,1} c_{2,2} c_{2,3}
c_{3,1} c_{3,2} c_{3,3}

Output

If Takahashi's statement is correct, print Yes; otherwise, print No.

Sample Input 1

1 0 1
2 1 2
1 0 1

Sample Output 1

Yes

Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.

Sample Input 2

2 2 2
2 1 2
2 2 2

Sample Output 2

No

Takahashi is incorrect in this case.

Sample Input 3

0 8 8
0 8 8
0 8 8

Sample Output 3

Yes

Sample Input 4

1 8 6
2 9 7
0 7 7

Sample Output 4

No

Solution in Rust (1.15.1) (judge verdict: Accepted)

#!/usr/bin/env run-cargo-script

#![allow(unused_imports)]

use std::cmp;
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::fmt;
use std::io::{self, BufWriter, Read, StdinLock, Write};
use std::ops::{Add, Div, Mul, Sub};
use std::str::{self, FromStr};

fn solve(cs: Vec<(i32, i32, i32)>) -> bool {
    let da2 = cs[1].0 - cs[0].0;
    let da3 = cs[2].0 - cs[0].0;
    let db2 = cs[0].1 - cs[0].0;
    let db3 = cs[0].2 - cs[0].0;
    let p1 = cs[1].1 == cs[0].0 + da2 + db2;
    let p2 = cs[1].2 == cs[0].0 + da2 + db3;
    let p3 = cs[2].1 == cs[0].0 + da3 + db2;
    let p4 = cs[2].2 == cs[0].0 + da3 + db3;
    p1 && p2 && p3 && p4
}

fn main() {
    let stdin = io::stdin();
    let mut sc = Scanner::new(stdin.lock().bytes());
    println!("{}", if solve(sc.trios(3)) { "Yes" } else { "No" });
}

struct Scanner<R: Read> {
    buf: Vec<u8>,
    bytes: io::Bytes<R>,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(bytes: io::Bytes<R>) -> Self {
        Scanner {
            buf: Vec::with_capacity(1024),
            bytes: bytes,
        }
    }

    fn next<T: FromStr>(&mut self) -> T
    where
        <T as FromStr>::Err: fmt::Debug,
    {
        let buf = &mut self.buf;
        buf.clear();
        self.bytes
            .by_ref()
            .map(Result::unwrap)
            .skip_while(|&c| c == ' ' as u8 || c == '\n' as u8)
            .take_while(|&c| !(c == ' ' as u8 || c == '\n' as u8))
            .foreach(|c| buf.push(c));
        str::from_utf8(&buf).unwrap().parse().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where
        <T as FromStr>::Err: fmt::Debug,
    {
        (0..n).map(|_| self.next()).collect()
    }

    fn pairs<T1: FromStr, T2: FromStr>(&mut self, n: usize) -> Vec<(T1, T2)>
    where
        <T1 as FromStr>::Err: fmt::Debug,
        <T2 as FromStr>::Err: fmt::Debug,
    {
        (0..n).map(|_| (self.next(), self.next())).collect()
    }

    fn trios<T1: FromStr, T2: FromStr, T3: FromStr>(&mut self, n: usize) -> Vec<(T1, T2, T3)>
    where
        <T1 as FromStr>::Err: fmt::Debug,
        <T2 as FromStr>::Err: fmt::Debug,
        <T3 as FromStr>::Err: fmt::Debug,
    {
        (0..n)
            .map(|_| (self.next(), self.next(), self.next()))
            .collect()
    }

    fn mat<T: FromStr>(&mut self, m: usize, n: usize) -> Vec<Vec<T>>
    where
        <T as FromStr>::Err: fmt::Debug,
    {
        (0..m).map(|_| self.vec(n)).collect()
    }

    fn strings_as_mat<T, F: FnMut(u8) -> T>(&mut self, h: usize, mut f: F) -> Vec<Vec<T>> {
        (0..h)
            .map(|_| {
                self.bytes
                    .by_ref()
                    .map(Result::unwrap)
                    .skip_while(|&c| c == ' ' as u8 || c == '\n' as u8)
                    .take_while(|&c| !(c == ' ' as u8 || c == '\n' as u8))
                    .map(&mut f)
                    .collect()
            })
            .collect()
    }
}

trait Foreach {
    type Item;
    fn foreach<F: FnMut(Self::Item)>(self, f: F);
}

impl<T, I: Iterator<Item = T>> Foreach for I {
    type Item = T;

    fn foreach<F: FnMut(T)>(self, mut f: F) {
        self.fold((), move |(), x| f(x));
    }
}