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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#[allow(unused_imports)]
use prcn_lib::{prelude::*, math, io, modint};

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

    let mut vic = vec![vec![]; n];
    for i in vic.iter_mut() {
        input! {
            a: usize,
            v: [(Usize1, usize); a]
        }
        *i = v;
    }

    // ありえる人数の最大値を探すための配列
    let mut ans = vec![0];
    // Bit全探索のBit, [0, 2 ^ n)
    'a: for case in 0..(1 << n) {
        let mut cond = vec![Condition::Unfound; n];

        for sft in 0..n {
            if (case >> sft) & 1 != 0 {
                match cond[sft] {
                    Condition::Unfound => cond[sft] = Condition::Honest,
                    Condition::Unkind => {
                        ans.push(0);
                        continue 'a;
                    }
                    Condition::Honest => {}
                }
            } else {
                match cond[sft] {
                    Condition::Unfound => cond[sft] = Condition::Unkind,
                    Condition::Unkind => {}
                    Condition::Honest => {
                        ans.push(0);
                        continue 'a;
                    }
                }
            }
            if (case >> sft) & 1 != 0 {
                for (who, b) in vic[sft].iter() {
                    match cond[*who] {
                        Condition::Unfound => cond[*who] = if *b == 1 { Condition::Honest } else { Condition::Unkind },
                        Condition::Honest => {
                            if *b == 0 {
                                ans.push(0);
                                continue 'a;
                            }
                        },
                        Condition::Unkind => {
                            if *b == 1 {
                                ans.push(0);
                                continue 'a;
                            }
                        }
                    }
                }
            }
        }
        ans.push(cond.iter().filter(|x| **x != Condition::Unkind).count())
    }

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

#[derive(Copy, Clone, PartialEq)]
enum Condition {
    Honest,
    Unkind,
    Unfound,
}
*/

fn main() {
    let exe = "/tmp/bin438BB065";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";