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)

c = Array.new(3) {Array.new(3,0)}
3.times do |i|
  tmp = gets.split("\s").map {|s|s.to_i}
  c[i][0] = tmp[0]
  c[i][1] = tmp[1]
  c[i][2] = tmp[2]
end

d00 = c[0][0] - c[1][0]
d10 = c[1][0] - c[2][0]
d20 = c[2][0] - c[0][0]
d01 = c[0][1] - c[1][1]
d11 = c[1][1] - c[2][1]
d21 = c[2][1] - c[0][1]
d02 = c[0][2] - c[1][2]
d12 = c[1][2] - c[2][2]
d22 = c[2][2] - c[0][2]

if d00==d01 && d01==d02 && d02==d00 &&
   d10==d11 && d11==d12 && d12==d10 &&
   d20==d21 && d21==d22 && d22==d20 then
  puts "Yes"
else
  puts "No"
end