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 (1.42.0) (judge verdict: Accepted)

use proconio::*;

fn main() {
    input! {
        c: [[i64; 3]; 3],
    };

    let mut ans = false;

    'outer: for a1 in 0..=100 {
        for a2 in 0..=100 {
            for a3 in 0..=100 {
                let b1_1 = c[0][0] - a1;
                let b2_1 = c[0][1] - a1;
                let b3_1 = c[0][2] - a1;
                let b1_2 = c[1][0] - a2;
                let b2_2 = c[1][1] - a2;
                let b3_2 = c[1][2] - a2;
                let b1_3 = c[2][0] - a3;
                let b2_3 = c[2][1] - a3;
                let b3_3 = c[2][2] - a3;

                if b1_1 == b1_2
                    && b1_3 == b1_1
                    && b2_1 == b2_2
                    && b2_3 == b2_1
                    && b3_1 == b3_2
                    && b3_3 == b3_1
                    && b1_1 <= 100
                    && 0 <= b1_1
                    && b2_1 <= 100
                    && 0 <= b2_1
                    && b3_1 <= 100
                    && 0 <= b3_1
                {
                    ans = true;
                    break 'outer;
                }
            }
        }
    }

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