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>
#define TABLESIZE 3 //おまけでテーブルの可変化を実装
#define BUFFSIZE TABLESIZE*(TABLESIZE+1)

int main() {
	//変数宣言。tblでマップフィールドを表現
	int i, j;
	int tbl[TABLESIZE][TABLESIZE];
	char buff[BUFFSIZE];

	//データ入力受付
	for (i = 0; i < TABLESIZE; i++) {
		fgets(buff, BUFFSIZE, stdin);
		sscanf(buff, "%d %d %d", &tbl[i][0], &tbl[i][1], &tbl[i][2]);
	}

	//一致の条件は(a(i)+b(j))-(a(i+1)+b(j))と
	//(a(i)+b(j+1))-(a(i+1)+b(j+1))を比較すれば求められるから以下の通りになる
	for (i = 0; i < TABLESIZE - 1; i++) {
		for (j = 0; j < TABLESIZE - 1; j++) {
			//条件を満たせなければ失敗とみなして終了する
			if (tbl[i][j] - tbl[i + 1][j] != tbl[i][j + 1] - tbl[i + 1][j + 1]) {
				printf("No\n");
				goto EndFanction;
			}
		}
	}
	printf("Yes\n");

EndFanction:
	return 0;
}