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::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let c11: isize = iterator.next().unwrap().parse().unwrap();
    let c12: isize = iterator.next().unwrap().parse().unwrap();
    let c13: isize = iterator.next().unwrap().parse().unwrap();
    let c21: isize = iterator.next().unwrap().parse().unwrap();
    let c22: isize = iterator.next().unwrap().parse().unwrap();
    let c23: isize = iterator.next().unwrap().parse().unwrap();
    let c31: isize = iterator.next().unwrap().parse().unwrap();
    let c32: isize = iterator.next().unwrap().parse().unwrap();
    let c33: isize = iterator.next().unwrap().parse().unwrap();

    let a1: isize = 0;
    let b1: isize = c11 - a1;
    let b2: isize = c12 - a1;
    let b3: isize = c13 - a1;

    if (c21 - b1) == (c22 - b2) && (c22 - b2) == (c23 - b3)
        && (c31 - b1) == (c32 - b2) && (c32 - b2) == (c33 - b3) {
        return String::from("Yes");
    }

    return String::from("No");
}