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)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let N: usize = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    };
    let (A, x, y) = {
        let mut A = vec![];
        let mut x = vec![];
        let mut y = vec![];
        for i in 0..N {
            let a: usize = {
                let mut line: String = String::new();
                std::io::stdin().read_line(&mut line).unwrap();
                line.trim().parse().unwrap()
            };
            A.push(a);
            let (X, Y): (Vec<usize>, Vec<usize>) = {
                let (mut X, mut Y) = (vec![], vec![]);
                for _ in 0..a {
                    let mut line: String = String::new();
                    std::io::stdin().read_line(&mut line).unwrap();
                    let mut iter = line.split_whitespace();
                    X.push(iter.next().unwrap().parse().unwrap());
                    Y.push(iter.next().unwrap().parse().unwrap());
                }
                (X, Y)
            };
            x.push(X);
            y.push(Y);
        }
        (A, x, y)
    };

    let ans = (0..(1 << N)).map(|z| {
        if (0..N).all(|i| (z >> i) & 1 == 0 || (0..A[i]).all(|j| ((z >> (x[i][j] - 1)) & 1) ^ y[i][j] == 0)) {
            format!("{:b}", z).to_string().chars().filter(|&c| c == '1').count()
        } else {
            0
        }
    }).max().unwrap();

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