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: Time Limit Exceeded)

package main

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

const (
	n = 3
	m = 3
)

type C [][]int

func newC() C {
	var c C
	c = make([][]int, m)
	for i := 0; i < m; i++ {
		c[i] = make([]int, n)
	}

	return c
}

func (c C) check(a, b []int) bool {
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			if a[i]+b[j] != c[i][j] {
				return false
			}
		}
	}

	return true
}

func main() {
	var input []string

	sc := bufio.NewScanner(os.Stdin)
	for sc.Scan() {
		input = append(input, sc.Text())
	}

	c := newC()

	for i := 0; i < m; i++ {
		line := strings.Split(input[i], " ")
		for j := 0; j < n; j++ {
			vInt, _ := strconv.Atoi(line[j])
			c[i][j] = vInt
		}
	}

	mMax := make([]int, m)
	nMax := make([]int, n)

	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			if mMax[i] < c[i][j] {
				mMax[i] = c[i][j]
			}
		}
	}

	for i := 0; i < n; i++ {
		for j := 0; j < m; j++ {
			if nMax[i] < c[i][j] {
				nMax[i] = c[i][j]
			}
		}
	}

	a := make([]int, m)
	b := make([]int, n)

	for i := 0; i <= mMax[0]; i++ {
		a[0] = i
		for j := 0; j <= mMax[1]; j++ {
			a[1] = j
			for k := 0; k <= mMax[2]; k++ {
				a[2] = k
				for l := 0; l <= nMax[0]; l++ {
					b[0] = l
					for m := 0; m <= nMax[1]; m++ {
						b[1] = m
						for n := 0; n <= nMax[2]; n++ {
							b[2] = n

							if c.check(a, b) {
								fmt.Println("Yes")
								return
							}
						}
					}
				}
			}
		}
	}

	fmt.Println("No")
}