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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#define pb push_back
#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()
#define sz(a) int((a).size())
#define endl '\n'

using namespace std;

typedef vector<int> vi;
typedef pair<int,int> ii;
typedef long long ll;

int n;
bool ok = true;
vector<vector<ii>> v;
vector<int> vb;
bitset<30> vis;

void dfs(int x){
	if(vis[x])
		return;
	vis[x]=true;
	for(auto &u:v[x]){
		if(u.ss==1 && vb[u.ff]==0){
			vb[u.ff]=1;
			dfs(u.ff-1);
		}
		else if(u.ss==1 && vb[u.ff]==2)
			ok=false;
		else if(u.ss==0 && vb[u.ff]==0)
			vb[u.ff]=2;
		else if(u.ss==0 && vb[u.ff]==1)
			ok=false;
	}
}

int count(int x){
	int res=0;
	while(x){
		res++;
		x-=x&-x;
	}
	return res;
}

int32_t main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	//#ifndef ONLINE_JUDGE
	//freopen("input.txt","r",stdin);
	//freopen("output.txt","w",stdout);
	//#endif
	int ans=0;
	cin>>n;
	v = vector<vector<ii>>(n,vector<ii>());
	for(int i=0;i<n;++i){
		int a;
		cin>>a;
		v[i].resize(a);
		for(int j=0;j<a;++j){
			cin>>v[i][j].ff>>v[i][j].ss;
		}
	}
	for(int i=0;i<(1<<n);++i){
		vb = vector<int>(n+1,0);
		ok = true;
		vis.reset();
		for(int j=0;j<n;++j){
			if((i&(1<<j))!=0){
				vb[j+1]=1;
				for(int k=0;k<sz(v[j]);++k){
					if(v[j][k].ss==1 && vb[v[j][k].ff]==0)
						vb[v[j][k].ff]=1;
					else if(v[j][k].ss==0 && vb[v[j][k].ff]==0)
						vb[v[j][k].ff]=2;
				}
			}
		}
		for(int j=0;j<n;++j){
			if(vb[j+1]==1){
				dfs(j);
			}
		}
		if(ok && count(i) > count(ans))
			ans=i;
	}
	cout<<count(ans)<<endl;
	return 0;
}