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)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

struct Edge {
    tt: Vec<usize>,
    tf: Vec<usize>,
    ff: Vec<usize>,
}

impl Clone for Edge {
    fn clone(&self) -> Self {
        Edge {
            tt: self.tt.clone(),
            tf: self.tf.clone(),
            ff: self.ff.clone(),
        }
    }
}

fn f(u: usize, edges: &Vec<Edge>, b: bool, check: &mut Vec<Option<bool>>) -> bool {
    if let Some(t) = check[u] {
        if t != b {
            return false;
        } else {
            return true;
        }
    }

    check[u] = Some(b);
    let mut ret = true;
    if b {
        for v in &edges[u].tt {
            ret = ret && f(*v, edges, true, check);
        }
        for v in &edges[u].tf {
            ret = ret && f(*v, edges, false, check);
        }
    } else {
        for v in &edges[u].ff {
            ret = ret && f(*v, edges, false, check);
        }
    }

    ret
}

use std::cmp::max;

fn g(u: usize, n: usize, edges: &Vec<Edge>, check: &mut Vec<Option<bool>>) -> u32 {
    if u == n {
        return 0;
    }

    let mut check_tmp1 = check.clone();
    let mut check_tmp2 = check.clone();

    let ans1;
    if f(u, edges, true, &mut check_tmp1) {
        ans1 = g(u + 1, n, edges, &mut check_tmp1) + 1;
    } else {
        ans1 = 0;
    }

    let ans2;
    if f(u, edges, false, &mut check_tmp2) {
        ans2 = g(u + 1, n, edges, &mut check_tmp2);
    } else {
        ans2 = 0;
    }

    max(ans1, ans2)
}

fn main() {
    let n: usize = read();

    let mut edges: Vec<Edge> = vec![
        Edge {
            tt: vec![],
            tf: vec![],
            ff: vec![],
        };
        n
    ];

    for i in 0..n {
        let a: usize = read();
        for _ in 0..a {
            let xy: Vec<usize> = read_vec();
            let j = xy[0] - 1;
            if xy[1] == 1 {
                edges[i].tt.push(j);
                edges[j].ff.push(i);
            } else {
                edges[i].tf.push(j);
                edges[j].tf.push(i);
            }
        }
    }

    let mut check: Vec<Option<bool>> = vec![None; n];
    println!("{}", g(0, n, &edges, &mut check));
}