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;

fn main() {
    let mut buf = String::new();
    let stdin = std::io::stdin();
    stdin.lock().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();

    let mut claims: Vec<Vec<(usize, u8)>> = vec![vec![]; n];

    for i in 0..n {
        let a_i: u8 = iter.next().unwrap().parse().unwrap();
        for _ in 0..a_i {
            let xj = iter.next().unwrap().parse::<usize>().unwrap() - 1;
            let yj = iter.next().unwrap().parse::<u8>().unwrap();
            claims[i].push((xj, yj));
        }
    }

    let mut ans: u32 = 0;

    'curr_subset: for subset_bit in 0_u16..(1 << n) {
        let mut visit_bit: u16 = 0;
        let mut stack: Vec<usize> = (0..n).filter(|i| subset_bit & 1_u16<<i != 0).collect();
        for i in &stack {
            visit_bit |= 1_u16<<i;
        }

        while !stack.is_empty() {
            let b = stack.pop().unwrap();
            for &(x, y) in &(claims[b]) {
                if (y == 0 && subset_bit & 1<<x != 0) || (y == 1 && subset_bit & 1<<x == 0) {
                    continue 'curr_subset;
                }
                if y == 1 && visit_bit & 1<<x == 0 {
                    stack.push(x);
                    visit_bit |= 1<<x;
                }
            }
        }
        ans = std::cmp::max(ans, subset_bit.count_ones());
    }

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