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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

ary = []
3.times do |i|
    ary[i] = gets.split.map(&:to_i)
end
max_n = ary.flatten.max
0.upto(max_n) do |a1|
    0.upto(max_n) do |b1|
        0.upto(max_n) do |a2|
            0.upto(max_n) do |b2|
                a3 = ary[2][0] - b1
                b3 = ary[0][2] - a1
                if (a1 + b1 == ary[0][0] &&
                    a1 + b2 == ary[0][1] &&
                    a1 + b3 == ary[0][2] &&
                    a2 + b1 == ary[1][0] &&
                    a2 + b2 == ary[1][1] &&
                    a2 + b3 == ary[1][2] &&
                    a3 + b1 == ary[2][0] &&
                    a3 + b2 == ary[2][1] &&
                    a3 + b3 == ary[2][2])
                    puts 'Yes'
                    exit
                end
            end
        end
    end
end
puts 'No'