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 <vector>
#include <algorithm>

using namespace std;
int c[3][3];

int main()
{
  for(int i = 0; i < 3; i++)
    for(int j = 0; j < 3; j++)
      cin >> c[i][j];
  
  // Check b values
  for(int i = 0; i < 3; i++) {
    for(int j = 0; j < 3; j++) {
      vector<int> check;
      for(int k = 0; k < 3; k++)
        check.push_back(c[k][i]-c[k][j]);
      size_t cnt = std::count(check.begin(), check.end(), check[0]);
      if(cnt != 3) {
        cout << "No" << endl;
        return 0;
      }
    }
  }
  // Check a values
  for(int i = 0; i < 3; i++) {
    for(int j = 0; j < 3; j++) {
      vector<int> check;
      for(int k = 0; k < 3; k++)
        check.push_back(c[i][k]-c[j][k]);
      size_t cnt = std::count(check.begin(), check.end(), check[0]);
      if(cnt != 3) {
        cout << "No" << endl;
        return 0;
      }
    }
  }
  cout << "Yes" << endl;
  return 0;
}