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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main()
{
	int c_1[5];
	int c_2[5];
	int c_3[5];
	int i, j;
	int a, b;
	int goukei;
	int srsa, srsb;
	int a1, a2, a3, b1, b2, b3;

	for (i = 0; i < 3; i++)
		scanf("%d", &c_1[i]);
	for (i = 0; i < 3; i++)
		scanf("%d", &c_2[i]);
	for (i = 0; i < 3; i++)
		scanf("%d", &c_3[i]);

	if (c_1[0] >= c_2[0]) {
		a = c_1[0] - c_2[0];
		srsa = 0;
	}
	else {
		a = c_2[0] - c_1[0];
		srsa = 1;
	}

	if (c_1[0] >= c_1[1]) {
		b = c_1[0] - c_1[1];
		srsb = 0;
	}
	else {
		b = c_1[1] - c_1[0];
		srsb = 1;
	}

	goukei = c_1[0] + c_2[1] + c_3[2];

	if ((srsa == 0) && (srsb == 0)) {
		for (i = 0; i <= (a + 1) / 2; i++) {
			for (j = 0; j <= (b + 1) / 2; j++) {
				a1 = a - i;
				a2 = i;
				b1 = b - j;
				b2 = j;
				a3 = c_1[0] + c_2[0] + c_3[0] - 3*b1 - a1- a2;
				b3 = c_1[0] + c_1[1] + c_1[2] - 3*a1 - b1- b2;

				if (((a1 + b1) == c_1[0]) && ((a2 + b2) == c_2[1]) && ((a3 + b3) == c_3[2]) && ((a1 + b2) == c_1[1]) && ((a1 + b3) == c_1[2]) && ((a2 + b1) == c_2[0]) && ((a2 + b3) == c_2[2]) && ((a3 + b1) == c_3[0]) && ((a3 + b2) == c_3[1])) {
					printf("Yes");
					return 0;
				}
				else {
					printf("No");
					return 0;
				}
			}
		}
	}

	else if ((srsa == 1) && (srsb == 0)) {
		for (i = 0; i <= (a + 1) / 2; i++) {
			for (j = 0; j <= (b + 1) / 2; j++) {
				a1 = i;
				a2 = a - i;
				b1 = b - j;
				b2 = j;
				a3 = c_1[0] + c_2[0] + c_3[0] - 3*b1 - a1- a2;
				b3 = c_1[0] + c_1[1] + c_1[2] - 3*a1 - b1- b2;

				if (((a1 + b1) == c_1[0]) && ((a2 + b2) == c_2[1]) && ((a3 + b3) == c_3[2]) && ((a1 + b2) == c_1[1]) && ((a1 + b3) == c_1[2]) && ((a2 + b1) == c_2[0]) && ((a2 + b3) == c_2[2]) && ((a3 + b1) == c_3[0]) && ((a3 + b2) == c_3[1])) {
					printf("Yes");
					return 0;
				}
				else {
					printf("No"); 
					return 0;
				}
			}
		}

	} 

	else if ((srsa == 0) && (srsb == 1)) {
		for (i = 0; i <= (a + 1) / 2; i++) {
			for (j = 0; j <= (b + 1) / 2; j++) {
				a1 = a - i;
				a2 = i;
				b1 = j;
				b2 = b - j;
				a3 = c_1[0] + c_2[0] + c_3[0] - 3*b1 - a1- a2;
				b3 = c_1[0] + c_1[1] + c_1[2] - 3*a1 - b1- b2;

				if (((a1 + b1) == c_1[0]) && ((a2 + b2) == c_2[1]) && ((a3 + b3) == c_3[2]) && ((a1 + b2) == c_1[1]) && ((a1 + b3) == c_1[2]) && ((a2 + b1) == c_2[0]) && ((a2 + b3) == c_2[2]) && ((a3 + b1) == c_3[0]) && ((a3 + b2) == c_3[1])) {
					printf("Yes");
					return 0;
				}
				else {
					printf("No");
					return 0;
				}
			}
		}

	}

	else {
		for (i = 0; i <= (a + 1) / 2; i++) {
			for (j = 0; j <= (b + 1) / 2; j++) {
				a1 = i;
				a2 = a - i;
				b1 = j;
				b2 = b - j;
				a3 = c_1[0] + c_2[0] + c_3[0] - 3*b1 - a1- a2;
				b3 = c_1[0] + c_1[1] + c_1[2] - 3*a1 - b1- b2;

				if (((a1 + b1) == c_1[0]) && ((a2 + b2) == c_2[1]) && ((a3 + b3) == c_3[2]) && ((a1 + b2) == c_1[1]) && ((a1 + b3) == c_1[2]) && ((a2 + b1) == c_2[0]) && ((a2 + b3) == c_2[2]) && ((a3 + b1) == c_3[0]) && ((a3 + b2) == c_3[1])) {
					printf("Yes");
					return 0;
				}
				else {
					printf("No");
					return 0;
				}
			}
		}

	}


	return 0;
}