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::{input, fastout};

#[fastout]
fn main() {
    input! {
        c11: isize, c12: isize, c13: isize,
        c21: isize, c22: isize, c23: isize,
        c31: isize, c32: isize, c33: isize,
    }

    let a_32_1 = c31-c21;
    let a_32_2 = c32-c22;
    let a_32_3 = c33-c23;
    let a_21_1 = c21-c11;
    let a_21_2 = c22-c12;
    let a_21_3 = c23-c13;

    let b_32_1 = c13-c12;
    let b_32_2 = c23-c22;
    let b_32_3 = c33-c32;
    let b_21_1 = c12-c11;
    let b_21_2 = c22-c21;
    let b_21_3 = c32-c31;

    let flg = {
        a_32_1 == a_32_2 && a_32_2 == a_32_3 &&
        a_21_1 == a_21_2 && a_21_2 == a_21_3 &&
        b_32_1 == b_32_2 && b_32_2 == b_32_3 &&
        b_21_1 == b_21_2 && b_21_2 == b_21_3
    };

    if flg { println!("Yes") }
    else { println!("No") }
}