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)

def array_sub(left, right)
  res = []
  left.each_with_index do |num, i|
    res << num - right[i]
  end
  res
end

def contains_one(array)
  array.all?{|num| num == array[0] }
end

c1 = STDIN.gets.split(' ').map(&:to_i)
c2 = STDIN.gets.split(' ').map(&:to_i)
c3 = STDIN.gets.split(' ').map(&:to_i)

c_1 = [c1[0], c2[0], c3[0]]
c_2 = [c1[1], c2[1], c3[1]]
c_3 = [c1[2], c2[2], c3[2]]

subs = []
subs << array_sub(c1, c2)
subs << array_sub(c2, c3)
subs << array_sub(c_1, c_2)
subs << array_sub(c_2, c_3)

if subs.all?{|array| contains_one(array)}
  puts 'Yes'
else
  puts 'No'
end