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 Kotlin (1.0.0) (judge verdict: Accepted)


fun c88(args: Array<String>) {
    // a1 + b1, a1 + b2, a1 + b3
    // a2 + b1, a2 + b2, a2 + b3
    // a3 + b1, a3 + b2, a3 + b3
    val numList = args.map { it.split(" ").map { it.toInt() } }
    val satisfiable = (1..100)
            .any {
                val a1 = it
                val b1 = numList[0][0] - a1
                val b2 = numList[0][1] - a1
                val b3 = numList[0][2] - a1
                val a2 = numList[1][0] - b1
                val a3 = numList[2][0] - b1
                a1 + b1 == numList[0][0]
                        && a1 + b2 == numList[0][1]
                        && a1 + b3 == numList[0][2]
                        && a2 + b1 == numList[1][0]
                        && a2 + b2 == numList[1][1]
                        && a2 + b3 == numList[1][2]
                        && a3 + b1 == numList[2][0]
                        && a3 + b2 == numList[2][1]
                        && a3 + b3 == numList[2][2]
            }

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

fun main(args: Array<String>) {
    c88(readLineList())
}

fun readLineList(): Array<String> {
    val lineList = mutableListOf<String>()
    while (true) {
        val line = readLine()
        if (line.isNullOrBlank()) {
            break
        } else {
            lineList.add(line!!)
        }
    }
    return lineList.toTypedArray()
}