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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Control.Monad
main=do
 s<-replicateM 3 (map read.words<$>getLine)
 let p=100
     s1=[(x,y)|x<-[1..p],y<-[1..p],x+y==(s!!0)!!0]
     s2=[(x,y)|x<-map fst s1,y<-[1..p],x+y==(s!!0)!!1]
     s3=[(x,y)|x<-map fst s2,y<-[1..p],x+y==(s!!0)!!2]
     s4=[(x,y)|x<-[1..p],y<-map snd s1,x+y==(s!!1)!!0]
     s5=[(x,y)|x<-map fst s4,y<-map snd s2,x+y==(s!!1)!!1]
     s6=[(x,y)|x<-map fst s5,y<-map snd s3,x+y==(s!!1)!!2]
     s7=[(x,y)|x<-[1..p],y<-map snd s4,x+y==(s!!2)!!0]
     s8=[(x,y)|x<-map fst s7,y<-map snd s5,x+y==(s!!2)!!1]
     s9=[(x,y)|x<-map fst s8,y<-map snd s6,x+y==(s!!2)!!2]
 putStrLn$if null s9 then "No" else "Yes"