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 (1.14.1) (judge verdict: Wrong Answer)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func main() {
	scanInit()

	c := nextIntMat(3, 3)

	a0tri := c[0][0] + c[0][1] + c[0][2]
	a1tri := c[1][0] + c[1][1] + c[1][2]
	a2tri := c[2][0] + c[2][1] + c[2][2]
	for b0i := 0; b0i <= 100; b0i++ {
		for b1i := 0; b1i <= 100; b1i++ {
			for b2i := 0; b2i <= 100; b2i++ {
				bsum := b1i + b1i + b2i
				a0 := a0tri - bsum
				a1 := a1tri - bsum
				a2 := a2tri - bsum
				if a0 < 0 || a1 < 0 || a2 < 0 {
					continue
				}
				if a0 > 100 || a1 > 100 || a2 > 100 {
					continue
				}
				if a0%3 != 0 || a1%3 != 0 || a2%3 != 0 {
					continue
				}
				fmt.Println("Yes")
				return
			}
		}
	}

	fmt.Println("No")
	return

}

// ---- readfunc
func scanInit() {
	const cap = 200 * 1024 // default=64*1024
	var buf = make([]byte, cap)
	sc.Buffer(buf, cap)
	sc.Split(bufio.ScanWords)
	return
}
func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}
func nextIntMat(a int, b int) [][]int {
	mat := make([][]int, a)
	for i := 0; i < a; i++ {
		mat[i] = make([]int, b)
		for j := 0; j < b; j++ {
			mat[i][j] = nextInt()
		}
	}
	return mat
}