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::Read;
use std::io::stdin;
use std::str::FromStr;

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

    let mut vec: Vec<Vec<(usize, usize)>> = vec![];

    for _ in 0..n {
        let a: usize = read();
        let mut v = vec![];
        for _ in 0..a {
            let x: usize = read();
            let y: usize = read();
            v.push((x, y));
        }
        vec.push(v);
    }

    let bits = bit_search(n);
    let mut ans = vec![0];

    'top: for bit in bits {
        for (i, &b) in bit.iter().enumerate() {
            if b {
                for &(x, y) in &vec[i] {
                    let m = if y == 0 { false } else { true };
                    if bit[x - 1] != m {
                        continue 'top;
                    }
                }
            }
        }
        ans.push(bit.iter().filter(|&&k| k).count());
    }

    println!("{}", ans.iter().max().unwrap());
}

fn bit_search(n: usize) -> Vec<Vec<bool>> {
    let mut vec = Vec::with_capacity(2usize.pow(n as u32));
    for b in 0..1 << n {
        vec.push((0..n).map(|k| (b >> k) & 1 == 1).collect());
    }
    vec
}