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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws IOException{
		TakashiInfo solver = new TakashiInfo();
		solver.readInput();
		solver.solve();
		solver.writeOutput();
	}

	static class TakashiInfo {

		private int map[][] = new int[3][3];

		private Scanner scanner;
		private String output;

		public TakashiInfo() {
			scanner = new Scanner(System.in);
		}

		public void readInput() {
			for(int i=0; i<3; i++) {
				for(int j=0; j<3; j++) {
					map[i][j] = Integer.parseInt(scanner.next());
				}
			}
		}
		public void solve() {
			for(int i=0;i<3;i++) {
				for(int j=1; j<3; j++) {
					map[i][j]-= map[i][0];
				}
			}
			output = (map[0][1]==map[1][1] && map[1][1]==map[2][1] && map[0][2]==map[1][2] && map[1][2]==map[2][2])? "Yes":"No";
		}


		public void writeOutput() {
			System.out.println(output);
		}
	}

}