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;

fn read<T: std::str::FromStr>(
    stdin_lock: &mut std::io::StdinLock,
    buf: &mut Vec<u8>,
    delimiter: u8,
) -> T {
    buf.clear();
    let l = std::io::BufRead::read_until(stdin_lock, delimiter, buf).unwrap();
    buf.truncate(l - 1); // remove delimiter
    let s = unsafe { std::str::from_utf8_unchecked(&buf) };
    s.parse().unwrap_or_else(|_| panic!("read"))
}

fn main() {
    let stdin = std::io::stdin();
    let mut stdin_lock = stdin.lock();
    let mut buf: Vec<u8> = Vec::new();
    let n: usize = read(&mut stdin_lock, &mut buf, b'\n');
    let mut av: Vec<Vec<Option<bool>>> = vec![vec![None; n]; n];
    for i in 0..n {
        let an: usize = read(&mut stdin_lock, &mut buf, b'\n');
        for _ in 0..an {
            let k: usize = read(&mut stdin_lock, &mut buf, b' ');
            let b: usize = read(&mut stdin_lock, &mut buf, b'\n');
            av[i][k - 1] = Some(b == 1usize);
        }
    }

    let mut ans = 0;
    for i in 0..2usize.pow(n as u32) {
        let mut tbl = vec![false; n];
        for j in 0..n {
            if i & (1 << j) != 0 {
                tbl[j] = true;
            }
        }

        // let mut tbl1 = vec![0i32; n];
        let mut c = false;
        for j in 0..n {
            if tbl[j] {
                for k in 0..n {
                    if let Some(b) = av[j][k] {
                        if tbl[k] != b {
                            c = true;
                        }
                    }
                }
            }
        }
        if c {
            continue;
        }

        let a = tbl.iter().filter(|&&x| x == true).count();
        ans = max(ans, a);
    }
    println!("{}", ans);
}