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(unused)]
use std::io::Write;

#[allow(unused)]
macro_rules! debug {
    ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
    ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}

fn main() {
    let n: usize = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let s = s.trim_right().to_owned();
        s.parse().unwrap()
    };

    let mut testimonies: Vec<Vec<(usize, bool)>> = vec![vec![]; n];

    for i in 0..n {
        let a_i: usize = {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            let s = s.trim_right().to_owned();
            s.parse().unwrap()
        };

        for j in 0..a_i {
            let (x, y): (usize, usize) = {
                let mut s = String::new();
                std::io::stdin().read_line(&mut s).unwrap();
                let s = s.trim_right().to_owned();
                let mut ws = s.split_whitespace();
                let a = ws.next().unwrap().parse().unwrap();
                let b = ws.next().unwrap().parse().unwrap();
                (a, b)
            };

            let honest = y == 1;
            // 0-originに
            testimonies[i].push((x - 1, honest));
        }
    }

    let mut max = 0;
    'outer: for bits in 0..(1 << n) {
        let mut honest_count = 0;
        for i in 0..n {
            if is_honest(bits, i) {
                honest_count += 1;
                for &(x, y) in &testimonies[i] {
                    if is_honest(bits, x) != y {
                        // debugln!("{:0>8b}: ng, x = {}", bits, x);
                        continue 'outer;
                    }
                    // debugln!("{:0>8b}: ok", bits);
                }
            }
        }
        if max < honest_count {
            max = honest_count;
        }
    }

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

fn is_honest(bits: usize, i: usize) -> bool {
    bits & (1 << i) > 0
}