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 <bits/stdc++.h>
using namespace std;

bool check(vector< vector<int> >& C, int a1, int a2, int a3) {
  vector<int> A = {a2, a3};
  vector<int> B = {C[0][0] - a1, C[0][1] - a1, C[0][2] - a1};
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 3; j++) {
      if (A[i] + B[j] != C[i+1][j]) {
        return false;
      }
    }
  }
  return true;
}

int main() {
  int tmp;
  vector< vector<int> > C(3);
  for (int i = 0; i < 3; i++) {
    cin >> tmp; C[i].push_back(tmp);
    cin >> tmp; C[i].push_back(tmp);
    cin >> tmp; C[i].push_back(tmp);
  }
  for (int a1 = 0; a1 <= 100; a1++) {
    for (int a2 = 0; a2 <= 100; a2++) {
      for (int a3 = 0; a3 <= 100; a3++) {
        if (check(C, a1, a2, a3)) {
          cout << "Yes" << endl;
          return 0;
        }
      }
    }
  }
  cout << "No" << endl;
}