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::cmp::max;
use std::io::{self, BufRead};

fn main() {
    let stdin = io::stdin();
    let mut handle = stdin.lock();
    let mut buf = String::new();
    handle.read_line(&mut buf).unwrap();
    let N = buf.trim().parse::<usize>().unwrap();
    buf.clear();

    let mut tests = Vec::with_capacity(N);
    for _ in 0..N {
        handle.read_line(&mut buf).unwrap();
        let A = buf.trim().parse::<usize>().unwrap();
        buf.clear();

        let mut t = Vec::with_capacity(A);
        for _ in 0..A {
            handle.read_line(&mut buf).unwrap();
            let tup = {
                let tmp = buf
                    .trim()
                    .split_whitespace()
                    .map(|x| x.parse::<usize>().unwrap())
                    .collect::<Vec<_>>();
                (tmp[0] - 1, tmp[1] == 1)
            };
            t.push(tup);
            buf.clear();
        }
        tests.push(t);
    }

    let mut ans = 0;
    'outer: for i in 0..(1 << N) {
        let mut n_honests = 0;
        for j in 0..N {
            if i & (1 << j) != 0 {
                // j は正直者
                n_honests += 1;

                for &(x, y) in &tests[j] {
                    if y && (i & 1 << x) == 0 {
                        continue 'outer;
                    }
                    if !y && (i & 1 << x) != 0 {
                        continue 'outer;
                    }
                }
            }
        }
        // 矛盾がなければOK
        ans = max(ans, n_honests);
    }

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