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() {
    let mut c: Vec<Vec<i32>> = Vec::new();
    for _ in 0..3 {
        c.push(read_vec());
    }
    let d0 = c[0][1] - c[0][0];
    let d1 = c[0][2] - c[0][1];
    if c[1][1] - c[1][0] == d0 && c[2][1] - c[2][0] == d0
        && c[1][2] - c[1][1] == d1 && c[2][2] - c[2][1] == d1
    {
        println!("Yes");
    } else {
        println!("No");
    }
}

fn read_line() -> String {
    let stdin = std::io::stdin();
    let mut buf = String::new();
    stdin.read_line(&mut buf).unwrap();
    buf
}

fn read_vec<T>() -> Vec<T>
    where T: std::str::FromStr, T::Err: std::fmt::Debug
{
    read_line()
        .split(' ')
        .map(|a| a.trim().parse().unwrap())
        .collect()
}