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)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

fn main() {
    let mut cs = vec![];

    for _ in 0..3 {
        let xs: Vec<i64> = reads();
        cs.push(xs);
    }

    let mut res = true;
    'outer:
    for i in 0..3 {
        for j in 0..3 {
            let v0 = cs[i][0] - cs[j][0];
            let v1 = cs[i][1] - cs[j][1];
            let v2 = cs[i][2] - cs[j][2];

            let u0 = cs[0][i] - cs[0][j];
            let u1 = cs[1][i] - cs[1][j];
            let u2 = cs[2][i] - cs[2][j];

            if !(v0 == v1 && v1 == v2 && v2 == v0 && u0 == u1 && u1 == u2 && u2 == u0) {
                res = false;
                break 'outer;
            }
        }
    }

    println!("{}",
    if res {
        "Yes"
    }
    else {
        "No"
    });
}