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: Wrong Answer)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

pub fn read_n<T: FromStr>(n: usize) -> Vec<T> {
    read_n_logic::<T>(n, vec![])
}

pub fn read_n_logic<T: FromStr>(n: usize, mut a: Vec<T>) -> Vec<T> {
    match n {
        0 => a,
        _ => {
            a.push(read::<T>());
            read_n_logic(n - 1, a)
        }
    }
}

struct UnionFind {
    parent: Vec<usize>,
    size: Vec<usize>,
}
impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind {
            parent: (0..n).collect(),
            size: vec![1; n],
        }
    }
    fn find(&mut self, x: usize) -> usize {
        if self.parent[x] == x {
            x
        } else {
            let p = self.parent[x];
            self.parent[x] = self.find(p);
            self.parent[x]
        }
    }
    fn union(&mut self, x: usize, y: usize) -> bool {
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x == y {
            false
        } else {
            if self.size[x] < self.size[y] {
                std::mem::swap(&mut x, &mut y);
            }
            self.parent[y] = x;
            self.size[x] += self.size[y];
            true
        }
    }
    fn size(&mut self, x: usize) -> usize {
        let p = self.find(x);
        self.size[p]
    }
}

use std::cmp::{max, min};

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

  let mut map: Vec<Vec<i64>> = vec![];
  let mut uf = UnionFind::new(n);

  for _ in 0..n {
    let a: i64 = read();
    let mut arr = vec![-1; n as usize];
    for _ in 0..a {
      let x: usize = read();
      let y: i64 = read();
      arr[x-1] = y
    }
    map.push(arr);
  }


  for i in &map {
    // println!("{:?}", i);
  };

  let mut cnt = n;

  for (i, v) in map.iter().enumerate() {
    for (j, v2) in v.iter().enumerate() {
      // println!("i: {}, j: {}, v2: {}", i, j, v2);
      if *v2 == 1 && map[j][i] == 0 {
        cnt -= 1;
        break;
      }

      if *v2 == 0 && map[j][i] == 0 {
        if j < i {
          cnt -= 1
        } 
      }

      if *v2 == 1 && map[j][i] == 1 {
        uf.union(i as usize, j as usize);
      }
    }
  }

  // for (i, v) in map.iter().enumerate() {
  //   for (j, v2) in v.iter().enumerate() {
  //     println!("i: {}, j: {}, v2: {}", i, j, v2);
  //     if *v2 == 0 && map[j][i] == 0 {
  //       cnt -= 1;
  //       break;
  //     }
  //   }
  // }

  let mut vmax = 0;

  for i in 0..n {
    vmax = max(vmax, uf.size(i)) 
  }

  println!("{}", min(cnt, vmax));
  

}