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;
typedef long long ll;

const string YES = "Yes";
const string NO = "No";

/*
void solve(std::vector<std::vector<long long>> c){
    ll left = c[0][0] + c[1][1] + c[2][2];
    ll right = c[0][2] + c[1][1] + c[2][0];
    ll all = (c[0][0] + c[0][1] + c[0][2] + c[1][0] + c[1][1] + c[1][2] + c[2][0] + c[2][1] + c[2][2]) % 3;
    if(left == right && all == 0) cout << YES << endl;
    else cout << NO << endl;
}
*/

void solve(std::vector<std::vector<long long>> c){
    if(c[1][0] - c[0][0] == c[1][1] - c[0][1] && c[1][1] - c[0][1] == c[1][2] - c[0][2] && c[2][0] - c[0][0] == c[2][1] - c[0][1] && c[2][1] - c[0][1] == c[2][2] - c[0][2]) cout << YES << endl;
    else cout << NO << endl;
}

int main(){
    std::vector<std::vector<long long>> c(3, std::vector<long long>(3));
    for(int i = 0 ; i < 3 ; i++){
        for(int j = 0 ; j < 3 ; j++){
            scanf("%lld",&c[i][j]);
        }
    }
    solve(std::move(c));
    return 0;
}