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;

struct Remark {
    person: u64,
    honest: bool
}

fn input<T:FromStr>() -> T {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.trim().parse().ok().unwrap()
}

fn input_tuple() -> (u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn main() {
    let n: usize = input();
    let mut remarks: Vec<Vec<Remark>> = Vec::new();

    for _ in 0..n {
        remarks.push(Vec::new());
    }

    for i in 0..n {
        let a: usize = input();
        for _ in 0..a {
            let (person, honest)= input_tuple();
            remarks[i].push(Remark {person: person - 1, honest: honest == 1});
        }
    }

    let mut max = 0;
    for bit in 0..1<<n {
        let mut honests: Vec<usize> = Vec::new();
        let mut not_honests: Vec<usize> = Vec::new();
        for i in 0..n {
            if bit & (1<<i) != 0 {
                honests.push(i);
            } else {
                not_honests.push(i);
            }
        }
        let mut valid = true;
        for honest in &honests {
            let mut flag = true;
            for remark in &remarks[*honest] {
                if remark.honest {
                    if not_honests.contains(&(remark.person as usize)) {
                        flag = false;
                    }
                } else {
                    if honests.contains(&(remark.person as usize)) {
                        flag = false;
                    }
                }
            }
            if !flag {
                valid = false;
                break;
            }
        }
        if valid {
            if honests.len() > max {
                max = honests.len();
            }
        }
    }
    println!("{}", max);
}