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 solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n: usize = sc.read();
    let test: Vec<Vec<(usize, bool)>> = (0..n)
        .map(|_| {
            (0..sc.read())
                .map(|_| (sc.read::<usize>() - 1, sc.read::<i32>() == 1))
                .collect()
        })
        .collect();

    let mut ans = 0;
    for bv in pow_bitvec(n) {
        let mut pc = 0;
        let ok = (0..n).filter(|&i| bv[i]).all(|i| {
            pc += 1;
            test[i].iter().all(|&(x, y)| bv[x] == y)
        });
        if ok && pc > ans {
            ans = pc;
        }
    }

    format!("{}", ans)
}

fn main() {
    let mut buf = String::new();
    use std::io;
    use std::io::{Read, Write};
    io::stdin().read_to_string(&mut buf).unwrap();
    io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}

struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}

#[derive(Clone)]
pub struct TinyBitVec(u64);

impl TinyBitVec {
    pub fn new() -> Self {
        TinyBitVec(0)
    }

    pub fn count_ones(&self) -> usize {
        self.0.count_ones() as usize
    }

    pub fn set(&mut self, i: usize, x: bool) {
        if x {
            self.0 |= 1 << i
        } else {
            self.0 &= !(1 << i)
        }
    }
}

const TRUE: &'static bool = &true;
const FALSE: &'static bool = &false;
impl std::ops::Index<usize> for TinyBitVec {
    type Output = bool;
    fn index(&self, index: usize) -> &bool {
        if (self.0 >> index) & 1 == 1 {
            TRUE
        } else {
            FALSE
        }
    }
}

pub fn pow_bitvec(n: usize) -> PowBitVec {
    assert!(n < 64);
    PowBitVec { c: 0, m: 1 << n }
}

pub struct PowBitVec {
    c: u64,
    m: u64,
}

impl Iterator for PowBitVec {
    type Item = TinyBitVec;

    fn next(&mut self) -> Option<Self::Item> {
        if self.c < self.m {
            let ret = TinyBitVec(self.c);
            self.c += 1;
            Some(ret)
        } else {
            None
        }
    }
}