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)

object Main extends App {
	val c = Array.ofDim[Int](3,3)

	for(i<-0 until 3){
		c(i) = scala.io.StdIn.readLine.split(" ").map(_.toInt)
	}


	val d1 = c(0)(0) - c(0)(1)
	val d2 = c(1)(0) - c(1)(1)
	val d3 = c(2)(0) - c(2)(1)

	val d4 = c(0)(0) - c(0)(2)
	val d5 = c(1)(0) - c(1)(2)
	val d6 = c(2)(0) - c(2)(2)

	val d7 = c(0)(1) - c(0)(2)
	val d8 = c(1)(1) - c(1)(2)
	val d9 = c(2)(1) - c(2)(2)

	val e1 = c(0)(0) - c(1)(0)
	val e2 = c(0)(1) - c(1)(1)
	val e3 = c(0)(2) - c(1)(2)

	val e4 = c(1)(0) - c(2)(0)
	val e5 = c(1)(1) - c(2)(1)
	val e6 = c(1)(2) - c(2)(2)

	val e7 = c(0)(0) - c(2)(0)
	val e8 = c(0)(1) - c(2)(1)
	val e9 = c(0)(2) - c(2)(2)

	if(d1 == d2 && d1 == d3 && d4 == d5 && d4 == d6 && d7 == d9 && d7 == d8){
		if(e1 == e2 && e1 == e3 && e4 == e5 && e4 == e6 && e7 == e9 && e7 == e8){
			println("Yes")
		}else{
			println("No")
		}
	}else{
		println("No")
	}

}