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)

using namespace std;
#include<bits/stdc++.h>
#define BEGIN ios_base::sync_with_stdio(0);cin.tie(0)
#define END return EXIT_SUCCESS
#define FOR(I,A,B) for((I)=(A);(I)<(B);(I)++)
#define REP(I,N) FOR(I,0,N)
#define UP(I,A,B) for((I)=(A);(I)<=(B);(I)++)
#define DW(I,A,B) for((I)=(A);(I)>=(B);(I)--)
#define IN(P) cin>>(P)
#define IN2(P1,P2) cin>>(P1)>>(P2)
#define IN3(P1,P2,P3) cin>>(P1)>>(P2)>>(P3)
#define INS(I,N,V) REP(I,N) cin>>V[I]
#define INS2(I,N,V1,V2) REP(I,N) cin>>V1[I]>>V2[I];
#define INS3(I,N,V1,V2,V3) REP(I,N) cin>>V1[I]>>V2[I]>>V3[I];
#define OUT(P) cout<<P<<endl
#define OUT2(P1,P2) cout<<P1<<" "<<P2<<endl
#define OUT3(P1,P2,P3) cout<<P1<<" "<<P2<<" "<<P3<<endl
#define OUTS(I,N,V) REP(I,N) cout<<V[i]<<endl
#define ALL(C) (C).begin(),(C).end()
#define RALL(C) (C).rbegin(),(C).rend()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
typedef unsigned long ul;
const ul INF = 1LL<<60;
int c[9],a1,a2,a3,i;
inline void solve(){
  REP(i,3){
    cin>>c[3*i]>>c[3*i+1]>>c[3*i+2];
  }
  REP(a1,101)REP(a2,101)REP(a3,101){
    if((c[0]-a1)==(c[3]-a2)&&(c[3]-a2)==(c[6]-a3)&&
       (c[1]-a1)==(c[4]-a2)&&(c[4]-a2)==(c[7]-a3)&&
       (c[2]-a1)==(c[5]-a2)&&(c[5]-a2)==(c[8]-a3)){
         OUT("Yes");
         return;
       }
  }
  OUT("No");
}

int main(int argc,char**argv){
  BEGIN;
  solve();
  END;
}