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: Wrong Answer)

grid = readlines.map { |line| line.chomp.split.map(&:to_i) }

m = Hash.new { |k, v| k[v] = [] }

(0..9).each do |a|
  (0..9).each do |b|
     (0..9).each do |c|
        m[a] << [b , c] if a == b + c
     end
  end
end

numbers = []
grid.each do |line|
  line.each do |n|
    numbers += m[n].flatten
    numbers.uniq!
  end
end

numbers.repeated_permutation(6).each do |r|
  result = [0, 1, 2].all? do |ai|
    grid[ai][0] == r[ai] + r[3] &&
      grid[ai][1] == r[ai] + r[4] &&
      grid[ai][2] == r[ai] + r[5]
  end
  if result
    puts('Yes')
    exit
  end
end
puts('No')