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<cstdint>
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<set>
#include<map>
#include<queue>
#include<deque>
#include<stack>
#include<iterator>
#include<stack>
#include<cctype>
#include<climits>
#include<string>
#include<bitset>
#include<cfloat>
#include<iomanip>
#include<numeric>
#include<utility>
#include<initializer_list>


#define repi(i,start,end)for(int64_t (i)=(start);(i)<(end);++(i))
#define rep(i,end) repi((i),0,(end))
#define rfor(x, v) for(auto& (x) : (v))
#define iterate(itr, v) for(auto (itr)=(v).begin();(itr)!=(v).end();++(itr))
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define vin(v) rep(i,(v).size()) cin >> (v)[i];
#define vpin(v) rep(i,(v).size()) cin >> (v)[i].first >> (v)[i].second

using namespace std;
using Int = int64_t;
using pint = pair<Int, Int>;
using vint = vector<Int>;
using vvint = vector<vint>;
using vpint = vector<pint>;
using vstr = vector<string>;

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1;  } return 0;  }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1;  } return 0;  }
template<class T>void put_double(T a){cout<<setprecision(12);cout<<a<<"\n";}
template<class T,class U>void put_pair(pair<T,U>p){cout<<p.first<<" "<<p.second<< endl;}
template<class T>void println(T a){cout << a << "\n";}
template<class T>void put_line(T &v){iterate(itr,v){cout<<*itr<<((itr==--v.end())?"\n":" ");}}
// auto [x, y] = make_tuple(3, 4); => let (x, y) = (3, 4);


int n;
vint a;
vector<vpint> xys;

bool judge(const vint &v) {
    vint res(n, -1);
    rep(i, n) {
        if(v[i] > 0) {
            rfor(p, xys[i]) {
                int x = p.first, y = p.second;
                if(res[x] == -1) res[x] = y;
                else if(res[x] != y) {
                    return false;
                }
            }
        }
    }
    rep(i, n) {
        if(res[i] != -1 && res[i] != v[i]) return false;
    }
    return true;
}

void dfs(vint &v, int &res) {
    if(v.size() == n) {
        if(judge(v)) {
            int cnt = 0;
            rfor(x, v) if(x) cnt++;
            chmax(res, cnt);
        }
    } else {
        v.push_back(0);
        dfs(v, res);
        v.pop_back();
        v.push_back(1);
        dfs(v, res);
        v.pop_back();
    }
}

int main(void) {
    cin >> n;
    a.resize(n);
    xys.resize(n);
    rep(i, n) {
        cin >> a[i];
        xys[i].resize(a[i]);
        rep(j, a[i]) {
            cin >> xys[i][j].first >> xys[i][j].second;
            xys[i][j].first--;
        }
    }
    vint v;
    int ans = 0;
    dfs(v, ans);
    println(ans);
    return 0;
}