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 Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn

object Main extends App {

   val a = (0 until 3).map{ i => StdIn.readLine().split(' ').map(_.toInt)}.toArray
   
   // c11 - c21 - (c12 - c22)
   val b1 = a(0)(0) - a(1)(0) - (a(0)(1) - a(1)(1))

   // c12 - c22 - (c13 - c23)
   val b2 = a(0)(1) - a(1)(1) - (a(0)(2) - a(1)(2))
   
   // c21 - c31 - (c22 - c32)
   val b3 = a(1)(0) - a(2)(0) - (a(1)(1) - a(2)(1))

   // c22 - c32 - (c23 - c33)
   val b4 = a(1)(1) - a(2)(1) - (a(1)(2) - a(2)(2))

   println(if(b1 == 0 && b2 == 0 && b3 == 0 && b4 == 0) "Yes" else "No")
}