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 main(args: Array<String>) {
    val cList: List<List<Int>> = (0 until 3).map {
        readLine()?.split(" ")?.map { it.toInt() } ?: listOf()
    }
    for (a1 in 0..100) {
        for (a2 in 0..100) {
            for (a3 in 0..100) {
                val b1 = cList[0][0] - a1
                val b2 = cList[1][1] - a2
                val b3 = cList[2][2] - a3
                if (cList[0][1] == a1 + b2 &&
                    cList[0][2] == a1 + b3 &&
                    cList[1][0] == a2 + b1 &&
                    cList[1][2] == a2 + b3 &&
                    cList[2][0] == a3 + b1 &&
                    cList[2][1] == a3 + b2
                ) {
                    println("Yes")
                    return
                }
            }
        }
    }
    println("No")
}