Problem:
Score : 300 points

Problem Statement

There are N people numbered 1 to N. Each of them is either an honest person whose testimonies are always correct or an unkind person whose testimonies may be correct or not.

Person i gives A_i testimonies. The j-th testimony by Person i is represented by two integers x_{ij} and y_{ij}. If y_{ij} = 1, the testimony says Person x_{ij} is honest; if y_{ij} = 0, it says Person x_{ij} is unkind.

How many honest persons can be among those N people at most?

Constraints

All values in input are integers.

1 \leq N \leq 15

0 \leq A_i \leq N - 1

1 \leq x_{ij} \leq N

x_{ij} \neq i

x_{ij_1} \neq x_{ij_2} (j_1 \neq j_2)

y_{ij} = 0, 1

Input

Input is given from Standard Input in the following format:

N
A_1
x_{11} y_{11}
x_{12} y_{12}
:
x_{1A_1} y_{1A_1}
A_2
x_{21} y_{21}
x_{22} y_{22}
:
x_{2A_2} y_{2A_2}
:
A_N
x_{N1} y_{N1}
x_{N2} y_{N2}
:
x_{NA_N} y_{NA_N}

Output

Print the maximum possible number of honest persons among the N people.

Sample Input 1

3
1
2 1
1
1 1
1
2 0

Sample Output 1

2

If Person 1 and Person 2 are honest and Person 3 is unkind, we have two honest persons without inconsistencies, which is the maximum possible number of honest persons.

Sample Input 2

3
2
2 1
3 0
2
3 1
1 0
2
1 1
2 0

Sample Output 2

0

Assuming that one or more of them are honest immediately leads to a contradiction.

Sample Input 3

2
1
2 0
1
1 0

Sample Output 3

1

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

//uses crt;
var n,i,o,p,k,l,j,m,x,z,count,max:longint;
used:array[1..16] of boolean;
type persoana = record
        testi:integer;
        saidabout:array[1..16] of integer;
        heis:array[1..16] of boolean;
        sincere:boolean;
        someonesaid:boolean;
        used:boolean;
        end;
var om:array[1..16] of persoana;
procedure backtrack(step:longint);
var i,o,p,k,j,curent:longint;
contradiction:boolean;
begin
if step=n+1 then begin
        contradiction:=false;
        k:=0;
        for i:=1 to n do
                om[i].sincere:=false;
                om[i].someonesaid:=false;
        for i:=1 to n do
                if used[i] then begin
                        inc(k);
                        om[i].sincere:=true;
                        om[i].someonesaid:=true;
                        //write(i,' ');
                        end;
               // writeln;
        for i:=1 to n do begin
                if contradiction then break;
                if om[i].sincere then
                        for j:=1 to om[i].testi do begin
                                curent:=om[i].saidabout[j];
                              //  writeln(curent);
                                if (om[curent].someonesaid) and (om[i].heis[j] <> om[curent].sincere) then begin
                                      //  writeln('omul',curent,' nu a zis nimeni si omul', i,' spune ca el este ',om[i].heis[j],' ceea ce este diferit de ',om[curent].sincere);
                                        contradiction:=true;
                                        break;
                                        end;
                                if (om[curent].someonesaid=false) and (om[curent].sincere <> om[i].heis[j]) then begin
                                        om[curent].sincere:=om[i].heis[j];
                                      //  writeln(curent);
                                        inc(K);
                                        end;
                                        end;
                                end;
      //  writeln(k,contradiction);
        if not contradiction then if k>max then max:=k;
        end
else begin
        used[step]:=true;
        backtrack(step+1);
        used[step]:=false;
        backtrack(step+1);
        end;
end;
begin
read(n);
for i:=1 to n do begin
        read(l);
        for j:=1 to l do begin
                read(x,z);
                om[i].saidabout[j]:=x;
                if z=1 then om[i].heis[j]:=true
                else om[i].heis[j]:=false;
              //  writeln(om[i].saidabout[j],' ',om[i].heis[j]);
                om[i].testi:=l;
                end;
        end;
backtrack(1);
writeln(max);
readln;
readln;
end.