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: Wrong Answer)

<?php

function parsenums($str) {
    return array_map(function ($a) {
        return intval($a);
    }, preg_split("/ /", $str));
}

$str1 = fgets(STDIN);
$str2 = fgets(STDIN);
$str3 = fgets(STDIN);

$r1 = parsenums($str1);
$r2 = parsenums($str2);
$r3 = parsenums($str3);

$c1n = array_sum($r1);
$c2n = array_sum($r2);
$c3n = array_sum($r3);

$cn1 = $r1[0] + $r2[0] + $r3[0];
$cn2 = $r1[1] + $r2[1] + $r3[1];
$cn3 = $r1[2] + $r2[2] + $r3[2];

function b() {
    global $cn1, $cn2, $cn3;
    $t1 = $cn1 + $cn2 - 2 * $cn3;
    foreach(range(0, 100) as $b1) {
        foreach(range(0, 100) as $b2) {
            foreach(range(0, 100) as $b3) {
                if(3 * $b1 + 3 * $b2 - 6 * $b3 == $t1) {
                    return true;
                }
            }
        }
    }
}

function a() {
    global $c1n, $c2n, $c3n;
    $t2 = $c1n + $c2n - 2 * $c3n;
    foreach(range(0, 100) as $a1) {
        foreach(range(0, 100) as $a2) {
            foreach(range(0, 100) as $a3) {
                if(3 * $a1 + 3 * $a2 - 6 * $a3 == $t2) {
                    return true;
                }
            }
        }
    }
}

if(a() && b()) {
    echo "Yes\n";
} else {
    echo "No\n";
}