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)

#![allow(unused_imports, unused_variables, dead_code)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;
use std::io::Write;

trait InputValue {
    fn parse(s: &str) -> Self;
}

fn read<T: InputValue>() -> T {
    let mut buf = String::new();
    let _ = stdin().read_line(&mut buf);
    T::parse(&buf.trim())
}

fn readvec<T: InputValue>() -> Vec<T> {
    let mut vec = vec![];
    let line: String = read();
    for token in line.split_whitespace() {
        vec.push(T::parse(token));
    }
    vec
}

fn readlines<T: InputValue>(n: usize) -> Vec<T> {
    let mut vec = vec![];
    for _ in 0..n {
        vec.push(read());
    }
    vec
}

macro_rules! parse_single_value {
    ($($t:ty),*) => {
        $(
            impl InputValue for $t {
                fn parse(s: &str) -> $t { s.parse().unwrap() }
            }
        )*
    }
}
parse_single_value!(i32, i64, f32, f64, usize, String);

macro_rules! parse_tuple {
    ($($t:ident),*) => {
        impl<$($t),*> InputValue for ($($t),*) where $($t: InputValue),* {
            fn parse(s: &str) -> ($($t),*) {
                let mut tokens = s.split_whitespace();
                ($($t::parse(tokens.next().unwrap())),*)
            }
        }
    }
}
parse_tuple!(A, B);
parse_tuple!(A, B, C);

// ===

fn ok(a: Vec<Vec<i32>>) -> bool {
    let c1 = a[0][1] - a[0][0];
    let c2 = a[0][2] - a[0][1];
    let r1 = a[1][0] - a[0][0];
    let r2 = a[2][0] - a[1][0];

    for i in 0..3 {
        if a[i][1] - a[i][0] != c1 {
            return false;
        }
        if a[i][2] - a[i][1] != c2 {
            return false;
        }
        if a[1][i] - a[0][i] != r1 {
            return false;
        }
        if a[2][i] - a[1][i] != r2 {
            return false;
        }
    }
    true
}

fn main() {
    let mut a: Vec<Vec<i32>> = vec![];
    for i in 0..3 {
        a.push(readvec());
    }

    if (ok(a)) {
        println!("Yes");
    } else {
        println!("No");
    }



}