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::*;

#[allow(dead_code)]
fn read<T: str::FromStr>() -> T {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|a| a.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_vec2d<T: str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn judge(bit: u32, vec: &Vec<Vec<(u32, u32)>>) -> bool {
    for i in 0..vec.len() {
        if bit & (1 << i) == 0 {
            continue;
        }
        for t in vec[i].iter() {
            let (x, y) = (t.0, t.1);
            match y {
                1 if bit & 1 << x == 0 => return false,
                0 if bit & 1 << x != 0 => return false,
                _ => continue,
            }
        }
    }
    true
}

fn main() {
    let n: u32 = read();
    let mut v: Vec<Vec<(u32, u32)>> = Vec::new();

    for _ in 0..n {
        let a: u32 = read();
        let mut v2: Vec<(u32, u32)> = Vec::new();
        for _ in 0..a {
            let tmp: Vec<u32> = read_vec();
            let (x, y) = (tmp[0], tmp[1]);
            v2.push((x, y));
        }
        v.push(v2);
    }

    println!("{:?}", v);

    let mut res = 0;
    for bit in 0..1 << n {
        if judge(bit, &v) {
            // let count = (0..n).fold(0, |cnt, i| if bit & (1 << i) != 0 { cnt + 1 } else { cnt });
            let mut count = 0;
            for i in 0..n {
                if bit & (1 << i) != 0 {
                    count += 1;
                }
            }
            res = cmp::max(res, count);
        }
    }
    println!("{}", res);
}