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::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: usize = read();
    let mut v: Vec< Vec< (usize, bool) >> = vec![vec![]; n];
    for i in 0..n {
        let a: usize = read();
        for _ in 0..a {
            let j: usize = read();
            let x: u8 = read();
            v[i].push((j-1, if x == 1 { true } else { false }));
        }
    }

    let mut ans: u8 = 0;

    for bit in 0..(1<<n) {
        let mut is_honest = vec![false; n];
        let mut cnt: u8  = 0;
        for i in 0..n {
            if bit & (1 << i) != 0 {
                is_honest[i] = true;
                cnt += 1;
            }
        }

        let mut ok = true;
        for i in 0..n {
            if !is_honest[i] {
                continue;
            }
            for j in 0..(v[i].len()) {
                if is_honest[v[i][j].0] != v[i][j].1 {
                    ok = false;
                    break;
                }
            }
            if !ok {
                break;
            }
        }
        
        if ok && ans < cnt {
            ans = cnt;
        }
    }

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