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: Runtime Error)

ary = []
3.times do
	ary << gets.chomp.split.map(&:to_i)
end

if ary.flatten.min < 0 then puts "No" end
if ary.flatten.max > 100 then puts "No" end

a = [0,0,0]
b = [0,0,0]
(ary[0].max+1).times do |n|
	a[0] = n
	b[0] = ary[0][0]-a[0]
	b[1] = ary[0][1]-a[0]
	b[2] = ary[0][2]-a[0]
	a[1] = ary[1][0]-b[0]
	a[2] = ary[2][0]-b[0]

	isCorrect = 0
	3.times do |na|
		3.times do |nb|
			if ary[na][nb] != a[na]+b[nb] then
				isCorrect = nil
			end
		end
	end
	if isCorrect then
		puts "Yes"
		return
	end
end
puts "No"