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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

#define vt          vector
#define sz(x)       int((x).size())
#define all(x)      (x).begin(), (x).end()
#define rall(x)     (x).rbegin(), (x).rend()
#define fi          first
#define se          second

using ll = long long;
using pii = pair<int, int>;

void solve() {
    vt<int> a(9);
    for (int &x : a) cin >> x;

    vt<int> b(3);
    for (int i = 0; i < 3; i++) {
        int mn = *min_element(a.begin() + i * 3, a.begin() + i * 3 + 3);
        for (int j = 0; j < 3; j++) {
            if (!i) b[j] = a[j] - mn;
            else if (b[j] != a[i * 3 + j] - mn)
                return void(cout << "No");
        }
    }

    cout << "Yes";
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);

    int tcs = 1;
    for (int tc = 1; tc <= tcs; tc++) {
        // cout << "Case " << tc << ": ";
        solve();
    }
}