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 (1.42.0) (judge verdict: Accepted)

use std::cmp::max;

fn input_one<T: std::str::FromStr> () -> Result<T, T::Err> {
    let mut n = String::new();
    std::io::stdin().read_line(&mut n).unwrap();
    n.trim().parse()
}

fn input_pair<T: std::str::FromStr + Copy> () -> (T, T) {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let arr: Vec<_> = s.trim().split_whitespace().flat_map(str::parse).collect();
    (arr[0], arr[1])
}

fn main() {
    let n: usize = input_one().unwrap();
    let mut cache = vec![vec![None; n]; n];
    for i in 0..n {
        let a: usize = input_one().unwrap();
        for _ in 0..a {
            let (x, y) = input_pair::<usize>();
            cache[x-1][i] = Some(y);
        }
    }
    let mut result = 0;
    for mask in 0..(1 << n) {
        let mut ok = true;
        let mut count = 0;
        for i in 0..n {
            let honest = (mask & (1 << i)) >> i;
            for (j, &test) in cache[i].iter().enumerate() {
                if mask & (1 << j) > 0 {
                    if test == None {
                        continue;
                    }
                    if test != Some(honest) {
                        ok = false;
                        break;
                    }
                }
            }
            if !ok {
                break;
            } else if honest == 1 {
                count += 1;
            }
        }
        if ok {
            result = max(result, count);
        }
    }
    println!("{}", result);
}