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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import Data.Array.IArray
import Data.Bits
import Data.Bool

import Debug.Trace
_t x = traceShow x x

bit2List :: Int -> Int -> [Int]
bit2List b n = go 0
  where
    go i | i  == n   = []
         | bi /= 0   = i : go (i+1)
         | otherwise = go (i+1)
      where bi = b .&. shift 1 i

solve :: Array Int [(Int,Int)] -> Int
solve a = maximum $ go1 (0 :: Int)
  where
    n = length a
    go1 b | b == shift 1 n = []
          | otherwise = go2 b : go1 (b+1)
    go2 b = let lb = bit2List b n
             in bool 0 (length lb) $ all f lb
      where
        f i = all g (a!i)
        g (x,y) = let p = b .&. shift 1 (x-1)
                   in ((y == 1 && p /= 0) || (y == 0 && p == 0))

main :: IO ()
main = do
    n <- readLn :: IO Int
    xy <- replicateM n $ do
        a <- readLn :: IO Int
        replicateM a $ do
            [x,y] <- map read . words <$> getLine :: IO [Int]
            return (x,y)
    let xy' = listArray (0,n-1) xy :: Array Int [(Int,Int)]
    print $ solve xy'