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 Rust (1.15.1) (judge verdict: Accepted)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

struct UnionFind{
    v: Vec<usize>
}

impl UnionFind{
    fn new(n: usize) -> UnionFind{
        let mut v: Vec<usize> = Vec::new();
        for i in 0..n{
         v.push(i);
        }
        UnionFind{v:v}
    }

    fn find(&mut self, i: usize) -> usize{
        if self.v[i] == i{
            i
        }else{
            let ni = self.v[i];
            self.v[i] = self.find(ni);
            self.v[i]
        }
    }

    fn union(&mut self, i: usize, j: usize){
        let root_i = self.find(i);
        let root_j = self.find(j);
        self.v[root_i] = root_j;
    }

}

fn list_all(v: &mut Vec<bool>, n: usize) -> Vec<Vec<bool>>{

    if v.len() == n{
        let mut res = v.clone();
        return vec![res];
    }

    let mut res = vec![];
    v.push(true);
    let mut tmp: Vec<Vec<bool>> = list_all(v, n);
    v.pop();
    res.append(&mut tmp);


    v.push(false);
    let mut tmp = list_all(v, n);
    v.pop();
    res.append(&mut tmp);

    return res;
}

fn check(graph: &Vec<Vec<(usize, bool)>>, pat: &Vec<bool>) -> bool{

    for i in 0..pat.len(){
        if pat[i] == false{
            continue;
        }
        for j in 0..graph[i].len(){
            let (target, chara) = (graph[i][j].0, graph[i][j].1);
            if chara != pat[target]{
                return false;
            }
        }
    }

    return true;
}

fn main(){
    let n = read_as_vec::<usize>()[0];

    let mut tests: Vec<Vec<(usize, bool)>> = vec![vec![];n];
    for i in 0..n{
        let a = read_as_vec::<usize>()[0];
        for _ in 0..a{
            let line = read_as_vec::<usize>();
            if line[1] == 1{
                let (x, y) = (line[0]-1, line[1]);
                tests[i].push((line[0]-1, true));
            }else{
                let (x, y) = (line[0]-1, line[1]);
                tests[i].push((line[0]-1, false));
            }
        }
    }

    //println!("{:?}", tests);
    let mut v = vec![];
    let possibles = list_all(&mut v, n);
    //println!("{:?}", possibles);


    let mut ans = 0;
    for pat in possibles{
        if check(&tests, &pat){

            ans = cmp::max(pat.iter().filter(|x| **x == true).count(), ans);
        }
    }

    println!("{}", ans);
}