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::io::Read;

struct Testmony {
    n: usize,
    x: Vec<usize>,
    y: Vec<usize>,
}

fn read(iter: &mut std::str::SplitWhitespace) -> Testmony {
    let n: usize = iter.next().unwrap().parse().unwrap();
    let mut t = Testmony {
        n: n,
        x: vec![],
        y: vec![],
    };
    for _ in 0..n {
        let x: usize = iter.next().unwrap().parse().unwrap();
        let y: usize = iter.next().unwrap().parse().unwrap();
        t.x.push(x - 1);
        t.y.push(y);
    }
    return t;
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let v: Vec<Testmony> = (0..n).map(|_| read(&mut iter)).collect();
    let mut ans = 0;
    for b in 0..1 << n {
        let mut a = vec![0; n];
        let mut cnt = 0;
        for i in 0..n {
            a[i] = (b >> i) & 1;
            cnt += (b >> i) & 1;
        }
        if ans >= cnt {
            continue;
        }
        let mut satisfy = true;
        for i in 0..n {
            if a[i] == 1 {
                let t = &v[i];
                for j in 0..t.n {
                    if a[t.x[j]] != t.y[j] {
                        satisfy = false;
                        break;
                    }
                }
            }
        }
        if satisfy {
            ans = cnt;
        }
    }

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