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 {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val rowC1 = readLine.split(" ").map(_.toInt)
    val rowC2 = readLine.split(" ").map(_.toInt)
    val rowC3 = readLine.split(" ").map(_.toInt)

    val maxN = 100

    def checkRow(row:Array[Int], a1: Int, a2: Int, a3:Int): Boolean ={
      ((row(0) - a1) == (row(1) - a2)) && ((row(1) - a2) == (row(2) - a3))
    }
    val checklist =
      for(a1 <- 0 to maxN; a2 <- 0 to maxN; a3 <- 0 to maxN) yield {
        val a = checkRow(rowC1, a1, a2, a3) && checkRow(rowC2, a1, a2, a3) && checkRow(rowC3, a1, a2, a3)
        //println("DEBUG" + a)
        a
      }
    val ans = checklist.exists(x => x)

    println(if(ans) "Yes" else "No")
  }

}