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)

fn read<T: std::str::FromStr>() -> Vec<T> {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    buf.split_whitespace()
        .map(|x| x.parse().ok().unwrap())
        .collect()
}
fn main() {
    let n: usize = read()[0];
    let v: Vec<Vec<Vec<usize>>> = (0..n)
        .map(|_| {
            let m: usize = read()[0];
            (0..m).map(|_| read()).collect()
        })
        .collect();

    let mut ans: usize = 0;
    for i in 0..2_usize.pow(n as u32) {
        let b: Vec<usize> = format!("{:0>1$b}", i, n)
            .chars()
            .map(|x| x.to_digit(10).unwrap() as usize)
            .collect();
        let mut res = true;
        let cnt = b.iter().filter(|&&x| x == 1).count();
        if cnt <= ans {
            continue;
        }

        for j in 0..n {
            if b[j] == 0 {
                continue;
            }
            if v[j].iter().all(|q| b[q[0] - 1] == q[1]) {
                continue;
            }

            res = false;
            break;
        }

        if res {
            ans = std::cmp::max(ans, cnt);
        }
    }
    println!("{}", ans);
}