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

$sc = new Scanner();
$out = new out();

for($i = 0; $i < 3; $i++) {
    $c[$i][0] = $sc->nextInt();
    $c[$i][1] = $sc->nextInt();
    $c[$i][2] = $sc->nextInt();
}

$da = $c[0][0] - $c[0][1];
$da2 = $c[0][1] - $c[0][2];

$db = $c[0][0] - $c[1][0];
$db2 = $c[1][0] - $c[2][0];

for($i = 0; $i < 3; $i++) {
    if ($c[$i][0] - $c[$i][1] !== $da || $c[$i][1] - $c[$i][2] !== $da2 || $c[0][$i] - $c[1][$i] !== $db || $c[1][$i] - $c[2][$i] !== $db2) {
        $out->println('No');exit;
    }
}
$out->println('Yes');


class Scanner {
    private $arr = [];
    private $count = 0;
    private $pointer = 0;
    public function next() {
        if($this->pointer >= $this->count) {
            $str = trim(fgets(STDIN));
            $this->arr = explode(' ', $str);
            $this->count = count($this->arr);
            $this->pointer = 0;
        }
        $result = $this->arr[$this->pointer];
        $this->pointer++;
        return $result;
    }
    public function hasNext() {
        return $this->pointer < $this->count;
    }
    public function nextInt() {
        return (int)$this->next();
    }
    public function nextDouble() {
        return (double)$this->next();
    }
}
class out {
    public static function println($str = "") {
        echo $str . PHP_EOL;
    }
}