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;
#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars};
#[allow(unused_imports)]
use std::cmp::{min, max};

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

	// 1行目でb1を基準としたb2,b3を求める
	let b2 = c[0][1] - c[0][0];
	let b3 = c[0][2] - c[0][0];
	// 2行目、3行目をチェック
	for i in 1..3 {
		if c[i][1] - c[i][0] != b2 || c[i][2] - c[i][0] != b3 {
			println!("No");
			return;
		}
	}

	// 1列目でa1を基準としたa2,a3を求める
	let a2 = c[1][0] - c[0][0];
	let a3 = c[2][0] - c[0][0];
	// 2列目、3列目をチェック
	for j in 1..3 {
		if c[1][j] - c[0][j] != a2 || c[2][j] - c[0][j] != a3 {
			println!("No");
			return;
		}
	}

	println!("Yes");
}