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)

c0 = gets.chomp.split(" ").map(&:to_i)
c1 = gets.chomp.split(" ").map(&:to_i)
c2 = gets.chomp.split(" ").map(&:to_i)

a01 = c1[0] - c0[0]
a02 = c2[0] - c0[0]

b01 = c0[1] - c0[0]
b02 = c0[2] - c0[0]

for a0 in 0..100 do
for b0 in 0..100 do
a1 = a0 + a01
a2 = a0 + a02
b1 = b0 + b01
b2 = b0 + b02
if
  c0[0] == a0 + b0 and
  c0[1] == a0 + b1 and
  c0[2] == a0 + b2 and
  c1[0] == a1 + b0 and
  c1[1] == a1 + b1 and
  c1[2] == a1 + b2 and
  c2[0] == a2 + b0 and
  c2[1] == a2 + b1 and
  c2[2] == a2 + b2 then
  puts "Yes"
  exit
end
end
end
puts "No"