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)

use std::io::prelude::*;

fn main() {
    let mut input_str = String::new();
    std::io::stdin().read_to_string(&mut input_str).unwrap();

    let input_parts = input_str.split_whitespace().collect::<Vec<_>>();
    let mut input_parts_it = input_parts.iter().cloned();
    let mut next = || input_parts_it.next().unwrap();

    let n: usize = next().parse().unwrap();

    struct Pr {
        and_mask: u16,
        bitmap: u16,
    }

    let prs = (0..n)
        .map(|_| {
            let a: usize = next().parse().unwrap();
            let mut and_mask: u16 = 0;
            let mut bitmap: u16 = 0;

            for _ in 0..a {
                let x: u32 = next().parse().unwrap();
                let y: u8 = next().parse().unwrap();
                and_mask |= 1u16 << x;
                if y != 0 {
                    bitmap |= 1u16 << x;
                }
            }

            Pr {
                and_mask: and_mask >> 1,
                bitmap: bitmap >> 1,
            }
        })
        .collect::<Vec<_>>();

    let best = (0..(1u16 << n))
        .filter(|&bitmap| {
            prs.iter().enumerate().all(|(i, pr)| {
                if (bitmap & (1 << i)) != 0 {
                    // validate his/her assertion
                    (bitmap & pr.and_mask) == pr.bitmap
                } else {
                    true
                }
            })
        })
        .map(|bitmap| bitmap.count_ones())
        .max()
        .unwrap();

    println!("{}", best);
}