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: Wrong Answer)

/* {{{ */
use std::io::*;
use std::str::FromStr;

struct Scanner<R: Read> {
    reader: R,
}

impl<R: Read> Scanner<R> {
    fn new(r: R) -> Scanner<R> {
        Scanner { reader: r }
    }
    fn read<T: FromStr>(&mut self) -> T {
        let token = self
            .reader
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok().unwrap()
    }
}
/* }}} */

use std::collections::HashMap;

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);
    let n: usize = sc.read();
    let mut m = HashMap::new();
    for i in 0..n {
        let a: usize = sc.read();
        let mut v = vec![None;n];
        for _ in 0..a {
            let x = sc.read::<usize>() - 1;
            let y = if sc.read::<usize>() == 0 {false} else {true};
            v[x] = Some(y);
        }
        m.insert(i,v);
    }
    let mut max = 0;
    for b in 0..(1u64 << n) {
        for i in 0..n {
            if b & (1 << i) == 0 { continue; }
            let iv = m.get(&i).unwrap();
            let mut cnt = 0;
            for j in 0..n {
                if i == j { continue; }
                if b & (1 << j) == 0 { continue; }
                let mut h = true;
                let jv = m.get(&j).unwrap();
                for k in 0..n {
                    if iv[k].is_some() && jv[k].is_some() &&
                       iv[k].unwrap() != jv[k].unwrap() {
                        h = false;
                        break;
                    }
                }
                if h { cnt += 1; }
            }
            max = std::cmp::max(max, cnt);
        }
    }
    println!("{}", max);
}
/* vim:set foldmethod=marker: */