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: Wrong Answer)

use std::collections::HashMap;

struct Testimony {
    people: usize,
    honest: bool,
}

fn main() {
    let mut _people_count = 0;

    let mut testimony: Vec<Vec<Testimony>> = Vec::new();

    let mut line: String = String::new();
    std::io::stdin().read_line(&mut line).unwrap();

    let mut honest_array: Vec<i32> = Vec::new();

    _people_count = line.trim().parse().unwrap();

    for _i in 0.._people_count {
        // 証言記録用のから配列を作る
        testimony.push(Vec::new());

        // とりあえず-1を
        honest_array.push(-1);
    }

    for i in 0.._people_count {
        let mut _testimony_count = 0;
        let mut line2: String = String::new();
        std::io::stdin().read_line(&mut line2).unwrap();
        _testimony_count = line2.trim().parse().unwrap();

        for _j in 0.._testimony_count {
            let mut line3: String = String::new();
            std::io::stdin().read_line(&mut line3).unwrap();

            // 読み込んだStringを空白で分解する
            let mut iter = line3.trim().split_whitespace();

            let people: usize = iter.next().unwrap().parse().unwrap();
            let honest_info: i32 = iter.next().unwrap().parse().unwrap();

            let honest = match honest_info {
                0 => false,
                1 => true,
                _ => true,
            };

            testimony[i].push(Testimony {
                people: people,
                honest: honest,
            });
        }
    }

    let mut max_honest = 0;
    let loop_count = 1 << _people_count;
    for k in 0..loop_count {
        let mut ok = true;
        for l in 0.._people_count {
            let assume_honest_parent = (k >> l) & 1;
            for m in (l + 1).._people_count {
                let assume_honest = (k >> m) & 1;
                if judge_contradiction(
                    &testimony[l],
                    &testimony[m],
                    !(assume_honest == assume_honest_parent),
                ) {
                    ok = false;
                    break;
                }
            }
        }
        if ok {
            let honest_count = {
                if k == 0 {
                    0
                } else {
                    let mut tmp_count = 0;
                    for kk in 0.._people_count {
                        if (k >> kk) & 1 == 1 {
                            tmp_count += 1;
                        }
                    }
                    tmp_count
                }
            };

            if honest_count > max_honest {
                max_honest = honest_count
            }
        }
    }

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

// 一人が正直、もう一人が不親切ならreverse=trueにする 矛盾したらtrueを返す
fn judge_contradiction(one: &Vec<Testimony>, two: &Vec<Testimony>, reverse: bool) -> bool {
    let mut info = HashMap::new();
    // 一人目を正しいと仮定
    for o in one.iter() {
        info.insert(o.people, o.honest);
    }

    for t in two.iter() {
        if !info.get(&t.people).is_none() {
            let one_honest = info.get(&t.people).unwrap();
            if reverse {
                if *one_honest == t.honest {
                    return true;
                }
            } else {
                if *one_honest != t.honest {
                    return true;
                }
            }
        }
    }

    return false;
}