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};
use proconio::marker::{Chars};
use proconio::marker::Usize1;
use std::cmp::*;

macro_rules! debug {
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

#[fastout]
fn main() {
    input!{
        c: [[usize; 3]; 3],
    }

    let mut tmp1 = 0;
    let mut tmp2 = 0;
    let mut tmp3 = 0;
    for i in 0..3 {
        for j in 0..3 {
            if i==0 {
                tmp1 += c[i][j];
            } else if i==1 {
                tmp2 += c[i][j];
            } else {
                tmp3 += c[i][j];
            }
        }
    }

    let mut tmp4 = 0;
    let mut tmp5 = 0;
    let mut tmp6 = 0;
    for j in 0..3 {
        for i in 0..3 {
            if j==0 {
                tmp4 += c[i][j];
            } else if j==1 {
                tmp5 += c[i][j];
            } else {
                tmp6 += c[i][j];
            }
        }
    }
    if (((tmp1 as i64) - (tmp2 as i64)).abs() % 3 == 0
     && ((tmp2 as i64) - (tmp3 as i64)).abs() % 3 == 0
     && ((tmp1 as i64) - (tmp3 as i64)).abs() % 3 == 0
     && ((tmp4 as i64) - (tmp5 as i64)).abs() % 3 == 0
     && ((tmp5 as i64) - (tmp6 as i64)).abs() % 3 == 0
     && ((tmp4 as i64) - (tmp6 as i64)).abs() % 3 == 0) {
        println!("Yes");
    } else {
        println!("No");
    }
    
}