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
$c[] = ints();
$c[] = ints();
$c[] = ints();
for ($a[0] = 0; $a[0] <= 100; $a[0]++) {
    $b[0] = $c[0][0] - $a[0];
    $b[1] = $c[0][1] - $a[0];
    $b[2] = $c[0][2] - $a[0];
    $a[1] = $c[1][0] - $b[0];
    $a[2] = $c[2][0] - $b[0];
    for ($i = 1; $i < 3; $i++) {
        for ($j = 1; $j < 3; $j++) {
            if ($c[$i][$j] !== $a[$i] + $b[$j]) continue 3;
        }
    }
    exit('Yes');
}
echo 'No';

function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}