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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use proconio::marker::Usize1;
use std::collections::BTreeSet;

fn main() {
    input! {
        n: usize
    }

    let mut mat = Vec::new();

    for _ in 0..n {
        input! {
            a: usize,
            x: [(Usize1,usize); a]
        }
        mat.push(x);
    }

    let ans = {
        let mut ans = 0;
        for b in 0..2u32.pow(n as u32) {
            let mut flag = true;
            let shojiki = (0..n).filter(|i| (b >> i) & 1 == 1).collect::<BTreeSet<usize>>();
            for &i in shojiki.iter() {
                if !flag {
                    break;
                }
                for &(j,whi) in &mat[i] {
                    if (shojiki.contains(&j) && whi == 0) || (!shojiki.contains(&j) && whi == 1) {
                        flag = false;
                        break;
                    }
                }
            }
            if flag && ans < shojiki.len() {
                ans = shojiki.len();
            }
        }
        ans
    };


    println!("{}",ans)
}