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)

c = [nil] * 3
3.times{|i| c[i] = gets.chomp.split(' ').map(&:to_i)}

def sub(v, u)
  w = [0] * 3
  3.times{|i| w[i] = v[i] - u[i]}
  return w
end

def parallel?(v, u)
  ( (v[0] * u[1] == v[1] * u[0]) and (v[1] * u[2] == v[2] * u[1]) )
end

def transpose(a)
  b = [nil] * 3
  3.times{|i| b[i] = [0] * 3}
  
  3.times do |i|
    b[i] = [0] * 3
    3.times{|j| b[j][i] = a[i][j]}
  end
  
  return b
end

d = transpose(c)

flags = [
  parallel?(sub(c[1], c[0]), sub(c[2], c[1])),
  parallel?(sub(c[2], c[1]), sub(c[0], c[2])),
  parallel?(sub(d[1], d[0]), sub(d[2], d[1])),
  parallel?(sub(d[2], d[1]), sub(d[0], d[2]))
]

puts (flags.all?{|x| x} ? 'Yes' : 'No')