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 <bits/stdc++.h>
using namespace std;

#define pq priority_queue
#define mp make_pair
#define cauto const auto &

#define REP(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i)
#define all(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())

#define clr(ar, val) memset(ar, val, sizeof(ar))

typedef long long int64;
typedef long long lint;
typedef long long lli;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;

typedef pair<int, int> pint;
typedef pair<long, long> plong;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
typedef pair<int, ll> pil;
typedef pair<ll, ll> pll;

const int iinf = 1 << 29;
const long long linf = 1ll << 61;

template <class T> bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T> bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T = int> T in() {
    T x;
    cin >> x;
    return (x);
}
template <class T> void print(T &x) {
    cout << x << '\n';
    return;
}

template <class T> ll sized_subset(T &comb) {
    T x = comb & -comb, y = x + comb;
    return ((comb & ~y) / x) >> 1 | y;
}

int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

int a[3],b[3],c[3][3];
int main() {
    REP(i,3){
        REP(j,3){
            c[i][j]=in();
        }
    }
    a[0]=c[0][0],b[0]=0;
    b[1]=c[1][0]-a[0];b[2]=c[2][0]-a[0];
    a[1]=c[0][1];a[2]=c[0][2];
    REP(i,2){
        REP(j,2){
            if(a[i+1]+b[j+1]!=c[j+1][i+1]){print("No");return 0;}
        }
    }
    print("Yes");
    return 0;
}