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;
use std::io::Write;

macro_rules! eprintln {
    ($($args:tt)*) => { let _ = writeln!(&mut std::io::stderr(), $($args)*); }
}

fn read_line() -> Vec<String> {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).expect("Failed to read line");
    line.trim().split_whitespace().map(|s| s.to_string()).collect()
}

struct Reader { v: Vec<String>, n: usize }

impl Reader {
    fn new() -> Self { Reader { v: read_line(), n: 0 } }
    fn next<T>(&mut self) -> T where T: std::str::FromStr, T::Err: std::fmt::Debug {
        if self.n == self.v.len() { self.v = read_line(); self.n = 0; }
        self.n += 1;
        self.v[self.n-1].parse().expect(&self.v[self.n-1])
    }
    #[allow(dead_code)]
    fn nexts<T>(&mut self, n: usize) -> Vec<T>
    where T: std::str::FromStr, T::Err: std::fmt::Debug {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n { v.push(self.next()); }
        v
    }
}

fn main() {
    let mut r = Reader::new();
    let n = r.next();
    let mut a = vec![0; n];
    let mut xy = Vec::new();
    for i in 0..n {
        a[i] = r.next();
        xy.push(vec![]);
        for j in 0..a[i] {
            let x: usize = r.next();
            let y: usize = r.next();
            xy[i].push((x-1, y));
        }
    }

    let mut ans = 0;
    for s in 0..(1 << n) {
        let mut ok = true;
        for i in 0..n {
            if ((s >> i) & 1) == 0 {
                continue;
            }
            for &(x, y) in xy[i].iter() {
                if ((s >> x) & 1) != y {
                    ok = false;
                }
            }
        }
        if ok {
            ans = max(ans, s.count_ones());
        }
    }

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