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 main() {
    const N: usize = 100;
    let c = read_vec2::<i32>(3);

    for i in 0..(N+1) {
        let mut a: Vec<i32> = vec![-1; 3];
        let mut b: Vec<i32> = vec![-1; 3];

        // a1
        a[0] = i as i32;
        // b1, b2, b3
        b[0] = c[0][0] - a[0];
        b[1] = c[0][1] - a[0];
        b[2] = c[0][2] - a[0];
        // a2, a3
        a[1] = c[1][0] - b[0];
        a[2] = c[2][0] - b[0];

        let mut ok = true;
        for j in 1..3 {
            for k in 1..3 {
                if c[j][k] != a[j] + b[k] {
                    ok = false;
                }
            }
        }
        if ok {
            println!("Yes");
            return;
        }
    }

    println!("No");
}

fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    let mut v2 = Vec::new();
    for _ in 0..n {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        let v = s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect();
        v2.push(v);
    }
    v2
}