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::vec::Vec;
use::std::collections::VecDeque;
use std::cmp::*;

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()
}

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

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

fn main() {
  let n: usize = read();
  let mut chart = vec![vec![]; n];
  for i in 0..n {
    let a: usize = read();
    for _ in 0..a {
      let (x, y) = read_touple::<usize>();
      chart[i].push((x-1, y));
    }
  }

  let mut ans: usize = 0;
  for i in 0..(1<<n) {
    if check(i, &chart) {
       ans = max(ans, counter(i));
    }
  }
  println!("{}", ans);
}

fn check(bit: usize, chart: &Vec<Vec<(usize, usize)>>) -> bool {
  let n = chart.len();
  for j in 0..n {
    if ((1<<j) & bit) != (1<<j) {
       continue
    }
    for &(x, y) in &chart[j] {
      if y == 0 && (bit & (1<<x)) == (1<<x) {
        return false
      } else if y == 1 && (bit & (1<<x) != (1<<x)) {
        return false
      }
    }
  }

  true
}

fn counter(bit: usize) -> usize {
  if bit == 0 {
    return 0;
  }
  counter(bit>>1) + (bit & 1)
}