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: Wrong Answer)

#include<iostream>
#include<string>
#include <vector>
#include<map>
#include<algorithm>
#include<iomanip>
#include<cmath>
#include<bitset>
using namespace std;
using vi = vector<int>;
using vii = vector<vi>;
using vs = vector<string>;
using pii = pair<int, int>;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define vsort(v) sort(v.begin(), v.end())
#define rv(v) reverse(v.begin(), v.end())
#define ll long long
using vll = vector<ll>;
const ll MOD = 1e9 + 7;

int main() {
	vii c(3, vi(3));
	rep(i, 3) {
		rep(j, 3) {
			cin >> c[i][j];
		}
	}
	vi a(3), b(3);
	a[0] = 0;
	rep(j, 3) b[j] = c[0][j];
	rep(i, 2) a[i + 1] = c[i + 1][0];
	bool flag = true;
	rep(i, 3) {
		rep(j, 3) {
			if (a[i] + b[j] != c[i][j]) flag = flag&&false;
		}
	}
	if (flag) cout << "Yes" << endl;
	else cout << "No" << endl;
}