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 JavaScript (node.js v5.12) (judge verdict: Accepted)

var lines = [];

var readline = require('readline');

var rl = readline.createInterface({
    input: process.stdin,
    output: process.stdout,
});

rl.on('line', function (x) {
    lines.push(x);
});

rl.on('close', function () {
    var c = lines.map(i => i.split(" ").map(i => Number(i)));
    
    // Aiを表す
    for (var a1 = 0; a1 <= 100; a1++) {
        var b1 = c[0][0] - a1
        var b2 = c[1][0] - a1
        var b3 = c[2][0] - a1

        // Biを表す
        for (var a2 = 0; a2 <= 100; a2++) {
            if (a2 + b1 !== c[0][1]) { continue }
            if (a2 + b2 !== c[1][1]) { continue }
            if (a2 + b3 !== c[2][1]) { continue }

            // Ciを表す
            for (var a3 = 0; a3 <= 100; a3++) {
                if (a3 + b1 !== c[0][2]) { continue }
                if (a3 + b2 !== c[1][2]) { continue }
                if (a3 + b3 !== c[2][2]) { continue }

                console.log("Yes");
                return (0)
            }
        }
    }
    console.log("No")

});