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: Accepted)

a = Array.new(3,0)
b = Array.new(3,0)
c = Array.new(3).map{Array.new(3,0)}
correct_flag = true

3.times do |i|
    c[i] = gets.split.map(&:to_i)
end

b[0] = (c[0][0] + c[1][0]) / 2
b[1] = ((c[0][0] + c[1][0]) / 2) - c[0][0] + c[0][1]
b[2] = ((c[0][0] + c[1][0]) / 2) - c[1][0] + c[1][2]

a[0] = c[0][0] - (c[0][0] + c[1][0]) / 2
a[1] = c[1][0] - (c[0][0] + c[1][0]) / 2
a[2] = c[2][0] - (c[0][0] + c[1][0]) / 2

for i in 0..2
    for j in 0..2
        if c[i][j] != (a[i] + b[j])
            correct_flag = false
        end
    end
end

if correct_flag
    puts "Yes"
else
    puts "No"
end