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 is_multiple_of_3?(array)
  sum = 0
  array.each do |line|
    sum += line.inject(:+)
  end
  sum % 3 == 0
end

def have_same_diffs?(array)
  diffs = []
  array.each do |line|
    diffs << [0, line[1] - line[0], line[2] - line[0]]
  end
  diffs[0] == diffs[1] && diffs[0] == diffs[2]
end

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

flag = true

# gridの9つの数字をすべて足し合わせると必ず3の倍数になっているはず。
flag = is_multiple_of_3?(grid) if flag

# 行ごとに見たとき、差分が3行とも一致しているはず
flag = have_same_diffs?(grid) if flag

# 列ごとに見たときも、差分が3行とも一致しているはず
flag = have_same_diffs?(grid.transpose) if flag

puts flag ? "Yes" : "No"