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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
	sc.Split(bufio.ScanWords)

	slice := make([][]int, 3)
	for i := 0; i < 3; i++ {
		slice[i] = make([]int, 3)
	}

	for i := 0; i < 3; i++ {
		for j := 0; j < 3; j++ {
			slice[i][j] = nextInt()
		}
	}

	// slice := [3][3]int{
	// 	{1, 0, 1},
	// 	{2, 1, 2},
	// 	{1, 0, 1},
	// }

	// fmt.Println(slice)

	a := make([]int, 3)
	b := make([]int, 3)
	a[0] = 0
	for i := 0; i < 2; i++ {
		for j := 0; j < 3; j++ {
			b[j] = slice[i][j] - a[i]
			a[i+1] = slice[i+1][j] - b[j]
		}
	}

	// fmt.Println(a)
	// fmt.Println(b)

	right := true

	for i := 0; i < 3; i++ {
		for j := 0; j < 3; j++ {
			if slice[i][j] != (a[i] + b[j]) {
				right = false
			}
		}
	}

	if right {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}