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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

const ROW_NUM = 3;
const COL_NUM = 3;

$input = [];
for ($i = 0; $i < ROW_NUM; $i++)
{
    $input[$i] = explode(' ', trim(fgets(STDIN)));
}

$result = true;

$a00 = (int)$input[0][0];
$a01 = (int)$input[0][1];
$a02 = (int)$input[0][2];

$a10 = (int)$input[1][0];
$diff = $a00 - $a10;

$a11 = (int)$input[1][1];
$result = $result && ($a01 - $a11 === $diff);
$a12 = (int)$input[1][2];
$result = $result && ($a02 - $a12 === $diff);

$a20 = (int)$input[2][0];
$diff = $a00 - $a20;
$a21 = (int)$input[2][1];
$result = $result && ($a01 - $a21 === $diff);
$a22 = (int)$input[2][2];
$result = $result && ($a02 - $a22 === $diff);

$diff = $a00 - $a01;
$result = $result && ($a10 - $a11 === $diff);
$result = $result && ($a20 - $a21 === $diff);

$diff = $a00 - $a02;
$result = $result && ($a10 - $a12 === $diff);
$result = $result && ($a20 - $a22 === $diff);

echo ($result)? 'Yes' : 'No';