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.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		//		new Main().solveA();
		//		new Main().solveB();
		new Main().solveC();
		// new Main().solveD();
		//		new Main().solveE();
		//		new Main().solveF();
	}

	private void solveA() {
		Scanner scanner = null;
		int numN = 0;
		int numA = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();
			numA = scanner.nextInt();

			int res = numN % 500;

			System.out.println(res <= numA ? "Yes" : "No");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private void solveB() {
		Scanner scanner = null;
		int numN = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();

			int[] wk = new int[numN];
			for (int i = 0; i < wk.length; i++) {
				wk[i] = scanner.nextInt();
			}

			Arrays.sort(wk);

			int alice = 0;
			int bob = 0;
			boolean convert = true;
			for (int i = wk.length - 1; i >= 0; i--) {
				if (convert) {
					alice += wk[i];
				} else {
					bob += wk[i];
				}
				convert = !convert;
			}

			System.out.println(alice - bob);

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private boolean chkC(int[][] wk, int max, int currentA, int[] aA, int[] bA) {
		if (currentA > max) {
			return false;
		}

		aA[0] = currentA;
		for (int j = 0; j < bA.length; j++) {
			bA[j] = wk[0][j] - currentA;
		}
		for (int i = 0; i < aA.length; i++) {
			aA[i] = wk[i][0] - bA[0];
		}
		boolean isMatch = true;
		outside: for (int i = 0; i < bA.length; i++) {
			for (int j = 0; j < bA.length; j++) {
				isMatch = wk[i][j] == aA[i] + bA[j];
				if (!isMatch) {
					break outside;
				}
			}
		}
		return isMatch ? true : chkC(wk, max, currentA + 1, aA, bA);
	}

	private void solveC() {
		Scanner scanner = null;

		try {
			scanner = new Scanner(System.in);

			int[][] wk = new int[3][3];
			int[] aA = new int[3];
			int[] bA = new int[3];

			int max = 0;
			for (int i = 0; i < wk.length; i++) {
				for (int j = 0; j < wk[i].length; j++) {
					wk[i][j] = scanner.nextInt();
					max = Math.max(max, wk[i][j]);
				}
			}

			System.out.println(chkC(wk, max, 0, aA, bA) ? "Yes" : "No");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private void solveD() {
		Scanner scanner = null;
		int numN = 0;
		int numK = 0;
		int numS = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();

			System.out.println("");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private void solveE() {
		Scanner scanner = null;
		int numN = 0;
		int numK = 0;
		int numS = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();

			System.out.println("");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}

	private void solveF() {
		Scanner scanner = null;
		int numN = 0;
		int numK = 0;
		int numS = 0;

		try {
			scanner = new Scanner(System.in);
			numN = scanner.nextInt();

			System.out.println("");

		} finally {
			if (scanner != null) {
				scanner.close();
			}
		}
	}
}