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)
c[0] = gets.split(/\s+/).map(&:to_i)
c[1] = gets.split(/\s+/).map(&:to_i)
c[2] = gets.split(/\s+/).map(&:to_i)

bd = Array.new(3)
ad = Array.new(3)

result = true

(0...3).each do |j|
  d1 = c[0][j] - c[0][(j + 1) % 3] 
  d2 = c[1][j] - c[1][(j + 1) % 3]
  d3 = c[2][j] - c[2][(j + 1) % 3]
  if d1 == d2 && d2 == d3
    bd[j] = d1
  else
    result = false
  end
end

(0...3).each do |i|
  d1 = c[i][0] - c[(i + 1) % 3][0]
  d2 = c[i][1] - c[(i + 1) % 3][1]
  d3 = c[i][2] - c[(i + 1) % 3][2]
  if d1 == d2 && d2 == d3
    ad[i] = d1
  else
    result = false
  end
end

if result
  if bd[0] + bd[1] + bd[2] == 0 && ad[0] + ad[1] + ad[2] == 0
    puts("Yes")
  else
    puts("No")
  end
else
  puts("No")
end