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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

    static PrintWriter out;
    static Scanner sc;

    static void solve() {
        int[][] c = new int[3][3];
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                c[i][j] = nextInt();
            }
        }

        int[] a = new int[3];
        int[] b = new int[3];

        // a[0]は固定値と想定して問題ない
        a[0] = 0;

        for (int j = 0; j <= 2; j++) {
            b[j] = c[0][j] - a[0];
        }
        for (int i = 1; i <= 2; i++) {
            a[i] = c[i][0] - b[0];
        }

        boolean ok = true;
        for (int i = 1; i <= 2; i++) {
            for (int j = 1; j <= 2; j++) {
                if (c[i][j] != a[i] + b[j]) {
                    ok = false;
                    break;
                }
            }
            if (!ok) {
                break;
            }
        }

        if (ok) {
            out.println("Yes");
        } else {
            out.println("No");
        }
    }

    static int nextInt() {
        return Integer.parseInt(sc.next());
    }

    static long nextLong() {
        return Long.parseLong(sc.next());
    }

    static String nextString() {
        return sc.next();
    }

    static int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    static List<Integer> nextIntList(int n) {
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(nextInt());
        }
        return list;
    }

    static List<Long> nextLongList(int n) {
        List<Long> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(nextLong());
        }
        return list;
    }

    static <T extends Comparable<? super T>> void sort(List<T> list) {
        Collections.sort(list);
    }

    // greatest common divisor
    static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    // baseのn乗を計算を返す
    static int pow(int base, int n) {
        int ret = 1;
        for (int i = 0; i < n; i++) {
            ret *= base;
        }
        return ret;
    }

    // intをlength桁のbit文字列に変換
    static String toBinaryString(int input, int length) {
        return toBinaryString(input).substring(29 - length);
    }

    // intを29桁のbit文字列に変換
    static String toBinaryString(int input) {
        String ret = "";
        int max = 0x10000000;
        for (int i = 0; i < 29; i++) {
            int tmp = input / max;
            ret += tmp;
            input %= max;
            max /= 2;
        }
        return ret;
    }

    public static void main(String[] args) {
        out = new PrintWriter(System.out);
        sc = new Scanner(System.in);

        solve();

        out.flush();
        sc.close();
    }

}