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)

///
// File:  c.go
// Author: ymiyamoto
//
// Created on Sun Feb 18 21:09:17 2018
//
package main

import (
	"fmt"
)

func main() {
	c := make([]int, 9)
	for i := 0; i < 9; i++ {
		fmt.Scan(&c[i])
	}

	for a1 := -1000; a1 <= 1000; a1++ {
		invalid := false
		b1 := c[0] - a1
		b2 := c[1] - a1
		b3 := c[2] - a1

		a2 := c[3] - b1
		if c[4]-b2 != a2 {
			invalid = true
		}
		if c[5]-b3 != a2 {
			invalid = true
		}

		a3 := c[6] - b1
		if c[7]-a3 != b2 {
			invalid = true
		}
		if c[8]-a3 != b3 {
			invalid = true
		}

		if !invalid {
			fmt.Println("Yes")
			return
		}
	}

	fmt.Println("No")

	return
}