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 check(people: &Vec<bool>, testimonials: &Vec<Vec<(usize, bool)>>) -> bool {
	for (i, p) in people.iter().enumerate() {
		if !p { continue };
		//println!("taking seriously {:?} {:?}", i, people);
		for testimonial in &testimonials[i] {
			//println!("testimonial: {:?}", testimonial);
			if people[testimonial.0-1] != testimonial.1 {
				return false
			}
		}
	}
	true
}

fn main() {
	let n: usize = read();
	let mut people = vec![false; n];

	let mut testimonials: Vec<Vec<(usize, bool)>> = Vec::new();
	for (i, p) in people.iter().enumerate() {
		let mut testimonial = Vec::new();
		for _ in 0..read() {
			let target: usize = read();
			let honest: usize = read();
			testimonial.push((target, honest == 1));
		}
		testimonials.push(testimonial);
	}

	let mut honest = 0;
	'outer: loop {
		let possible = check(&people, &testimonials);
		//println!("is possible? {:?} with people like {:?}", possible, people);
		if possible {
			let n_honest = people.iter().filter(|p| **p).count();
			//println!("n_honest: {:?}", n_honest);
			if n_honest > honest {
				honest = n_honest;
			}
		}

		for i in 0..people.len() {
			if people[i] == false {
				people[i] = true;
				break;
			}
			people[i] = false;
			if i == people.len() - 1 {
				break 'outer;
			}
		}
	}
	println!("{}", honest);
}