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)

use std::io::*;

fn main() {
    let i = stdin();
    solve(&mut i.lock(), &mut stdout());
}

fn solve(i: &mut BufRead, o: &mut Write) {
    let mut c = Vec::new();
    for _ in 0..3 {
        c.push(read_nums(i));
    }
    let r1 = c[2][2] - c[2][0] - c[1][2] + c[1][0] == 0;
    let r2 = c[2][2] - c[2][0] - c[1][2] + c[1][1] - c[0][1] + c[0][0] == 0;
    let r3 = -c[2][1] + c[2][0] + c[0][1] - c[0][0] == 0;
    let r4 = -c[2][2] + c[2][0] + c[0][2] - c[0][0] == 0;
    let r = r1 && r2 && r3 && r4;

    /*
    eliminate(
    [
    a0 + b0 = c00,
    a1 + b0 = c10,
    a2 + b0 = c20,

    a0 + b1 = c01,
    a1 + b1 = c11,
    a2 + b1 = c21,

    a0 + b2 = c02,
    a1 + b2 = c12,
    a2 + b2 = c22,
    ],
    [a0,a1,a2,b0,b1,b2])
    */

    writeln!(o, "{}", if r { "Yes" } else { "No" }).unwrap();
}

fn read_line(i: &mut BufRead) -> String {
    let mut line = String::new();
    i.read_line(&mut line).unwrap();
    line.trim().to_string()
}
fn read_nums(i: &mut BufRead) -> Vec<isize> {
    read_line(i)
        .split(' ')
        .map(|x| x.parse().unwrap())
        .collect()
}