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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <string>
#include <numeric>
#include <cmath>

typedef long long ll;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)

using namespace std;

bool isCorrect(int grid[3][3], int a1, int a2, int a3) {
    int j1, j2, j3;
    j1 = grid[0][0] - a1;
    j2 = grid[0][1] - a1;
    j3 = grid[0][2] - a1;

    if (a2 + j1 != grid[1][0]) return false;
    if (a2 + j2 != grid[1][1]) return false;
    if (a2 + j3 != grid[1][2]) return false;
    if (a3 + j1 != grid[2][0]) return false;
    if (a3 + j2 != grid[2][1]) return false;
    if (a3 + j3 != grid[2][2]) return false;

    return true;
}

int main(void) {
    int grid[3][3];
    REP(i, 3) {
        REP(j, 3) {
            cin >> grid[i][j];
        }
    }

    FOR(a1, 0, 101) {
        FOR(a2, 0, 101) {
            FOR(a3, 0, 101) {
                if (isCorrect(grid, a1, a2, a3)) {
                    cout << "Yes" << endl;
                    return 0;
                }
            }
        }
    }

    cout << "No" << endl;

    return 0;
}