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 Perl (v5.18.2) (judge verdict: Accepted)

my $c;
my $i = 1;
while (my $l = <STDIN>) {
        chomp $l;
        if ($l =~ m/^(\d*?) (\d*?) (\d*?)$/) {
                $c->{$i}->{1} = $1;
                $c->{$i}->{2} = $2;
                $c->{$i}->{3} = $3;
        }
        $i++;
}

my ($A, $B);
my $flag = 1;
     $A->{1}->{2} =  $c->{1}->{1}-$c->{2}->{1};
if (($A->{1}->{2} == $c->{1}->{2}-$c->{2}->{2})
 && ($A->{1}->{2} == $c->{1}->{3}-$c->{2}->{3})){
} else {
        $flag = 0;
}
     $A->{1}->{3} =  $c->{1}->{1}-$c->{3}->{1};
if (($A->{1}->{3} == $c->{1}->{2}-$c->{3}->{2})
 && ($A->{1}->{3} == $c->{1}->{3}-$c->{3}->{3})){
} else {
        $flag = 0;
}
     $A->{2}->{3} =  $c->{2}->{1}-$c->{3}->{1};
if (($A->{2}->{3} == $c->{2}->{2}-$c->{3}->{2})
 && ($A->{2}->{3} == $c->{2}->{3}-$c->{3}->{3})){
} else {
        $flag = 0;
}
     $B->{1}->{2} =  $c->{1}->{1}-$c->{1}->{2};
if (($B->{1}->{2} == $c->{2}->{1}-$c->{2}->{2})
 && ($B->{1}->{2} == $c->{3}->{1}-$c->{3}->{2})){
} else {
        $flag = 0;
}
     $B->{1}->{3} =  $c->{1}->{1}-$c->{1}->{3};
if (($B->{1}->{3} == $c->{2}->{1}-$c->{2}->{3})
 && ($B->{1}->{3} == $c->{3}->{1}-$c->{3}->{3})){
} else {
        $flag = 0;
}
     $B->{2}->{3} =  $c->{1}->{2}-$c->{1}->{3};
if (($B->{2}->{3} == $c->{2}->{2}-$c->{2}->{3})
 && ($B->{2}->{3} == $c->{3}->{2}-$c->{3}->{3})){
} else {
        $flag = 0;
}
if ($flag) {
        print "Yes\n";
} else {
        print "No\n";
}