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;
use std::str::FromStr;

fn main() {
    let table = read_table();
    println!("{}", if trust(&table) { "Yes" } else { "No" });
}

fn trust(t: &[Vec<i32>]) -> bool {
    // want something like zip
    let t0 = t[0][0];
    let da0 = t[0][1] - t[0][0];
    let da1 = t[0][2] - t[0][1];
    let db0 = t[1][0] - t[0][0];
    let db1 = t[2][0] - t[1][0];
    t[1][1] == t0 + da0 + db0 && t[1][2] == t[1][1] + da1 && t[2][1] == t[1][1] + db1
        && t[2][2] == t[2][1] + da1
}

fn read_table() -> Vec<Vec<i32>> {
    let mut table: Vec<Vec<i32>> = Vec::new();
    for _ in 0..3 {
        table.push(reads(&get_line()));
    }
    table
}

fn get_line() -> String {
    let mut inp = String::new();
    io::stdin().read_line(&mut inp).expect("read error");
    inp.trim().to_string()
}

fn reads<T>(input: &str) -> Vec<T>
where
    T: FromStr,
    T::Err: std::fmt::Debug,
{
    input
        .trim()
        .split_whitespace()
        .map(|n| n.parse().unwrap())
        .collect()
}