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<set>
#include<queue>
#include<bitset>
#define rep(i,j,n) for(int i=j;i<n;i++)
using namespace std;
#define int long long
struct edge{long long to,cost;};
struct st{int rate,way,num;};
typedef pair<int,int>P;
#define inf 1000000007
string alph("abcdefghijklmnopqrstuvwxyz");
signed main(){
    int num[3][3];
    rep(i,0,3)rep(j,0,3)cin>>num[i][j];
    bool ans=true;
    rep(i,0,2){
        if(num[i+1][0]-num[i][0]!=num[i+1][1]-num[i][1]||num[i+1][0]-num[i][0]!=num[i+1][2]-num[i][2])ans=false;
    }
    rep(i,0,2){
        if(num[0][i+1]-num[0][i]!=num[1][i+1]-num[1][i]||num[0][i+1]-num[0][i]!=num[2][i+1]-num[2][i])ans=false;
    }
    if(ans)cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
}