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: Wrong Answer)


fn main(){
	let mut v: Vec<Vec<i32>> = Vec::new();
	for i in 0..3 {
		v.push(Vec::new());
		let mut s = String::new();
		std::io::stdin().read_line(&mut s).unwrap();
		let vec: Vec<&str> = s.trim().split(' ').collect();
		for j in &vec {
			v[i].push(j.parse().unwrap());
		}
	}
	let mut flag = false;
	for i in 0..8 {
		let mut n = 0;
		for j in 0..3 {
			match i {
				0 | 1 | 2 => {
					n += v[0][j];
				},
				3 | 4 | 5 => {
					n += v[j][0];
				},
				6 => {
					n += v[j][j];
				},
				7 => {
					n += v[match j {
						0 => 2, 2 => 0, _ => 1,
					}][j];
				},
				_ => {},
			};
		}
		for y in &v {
			for x in y {
				if *x == n {
					flag = true;
				}
			}
		}
	}

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