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::collections::HashSet;

fn main() {
    let n = read::<usize>();
    let mut v: Vec<Vec<usize>> = vec![vec![usize::max_value(); n+1]; n+1];
    for i in 0..n {
        let a = read::<usize>();
        for _ in 0..a {
            let xy = read_vec::<usize>();
            v[i+1][xy[0]] = xy[1];
        }
    }

    let mut ma = 0;
    for bit in 0..1<<n {
        let mut hset: HashSet<usize> = HashSet::new();
        let mut nset: HashSet<usize> = HashSet::new();
        for i in 0..n {
            if bit & 1<<i != 0 {
                hset.insert(i+1);
            } else {
                nset.insert(i+1);
            }
        }

        let mut cnt = hset.len();
        for i in hset.iter() {
            let g = &v[*i];
            for j in 0..n {
                if g[j+1] == usize::max_value() { continue; }

                if g[j+1] == 1 {
                    if nset.contains(&(j+1)) {
                        cnt = 0;
                        break;
                    }
                } else {
                    if hset.contains(&(j+1)) {
                        cnt = 0;
                        break;
                    }
                }
            }
        }

        if ma < cnt {
            ma = cnt;
        }
    }

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

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}