C - Takahashi's Information

Time Limit: 2 sec / Memory Limit: 256 MB

﻿配点：300

### 問題文

3 \times 3 のグリッドがあります. 上から i 番目で左から j 番目のマスを (i, j) で表すとき, マス (i, j) には数 c_{i, j} が書かれています.

### 制約

• c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3)0 以上 100 以下の整数

### 入力

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}


### 入力例 1

1 0 1
2 1 2
1 0 1


### 出力例 1

Yes


a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1 などの組み合わせがありうるので, 高橋君の情報は正しいです.

### 入力例 2

2 2 2
2 1 2
2 2 2


### 出力例 2

No


このグリッドの場合、高橋君の情報は間違っています.

### 入力例 3

0 8 8
0 8 8
0 8 8


### 出力例 3

Yes


### 入力例 4

1 8 6
2 9 7
0 7 7


### 出力例 4

No


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