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<cstdio>
#include<iostream>
#include<cmath>
#include<cstring>
#include<cctype>
#include<cstdlib>
#include<algorithm>
#include<ctime>
#include<stack>
#include<queue>
#include<map>
#define size 300010
#define ll long long
#define db double
#define il inline
#define rint register int
#define gc getchar()
#define rep(i,s,n) for (register int i=s;i<=n;i++)
#define sro_zyb_orz int main()

using namespace std;

il ll r()
{
	char c; ll x,f=1;
	for (c=gc;!isdigit(c);c=gc) if (c=='-') f=-1; x=c-'0';
	for (c=gc;isdigit(c);c=gc) x=x*10+c-'0'; return x*f;
}

int c[5][5];


sro_zyb_orz
{
	rep(i,1,3) rep(j,1,3) c[i][j]=r();
	if (c[1][1]+c[2][2]+c[3][3]==c[1][3]+c[2][2]+c[3][1]
	&&c[1][3]+c[2][2]+c[3][1]==c[1][2]+c[2][3]+c[3][1]
	&&c[1][2]+c[2][3]+c[3][1]==c[1][3]+c[2][1]+c[3][2]) 
		cout<<"Yes"<<endl;
	else cout<<"No"<<endl;

	return 0;
}