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 8.8.3) (judge verdict: Accepted)

import Data.List
import qualified Data.Map as M
import Control.Monad

getInputData :: IO [(Int,Int)]
getInputData = do
 n <- read <$> getLine :: IO Int
 ans <- replicateM n ((\[x,y] -> (x-1,y)) . map read . words <$> getLine) 
 return ans

getHonestStatement ::  [[(Int, Int)]] -> [[(Int, Int)]] -> [Int] -> [[(Int, Int)]]
getHonestStatement statement ans choice
 | null choice = ans
 | otherwise   = getHonestStatement statement ((statement !! (head choice)):ans) (tail choice)
 
judge :: [(Int, Int)] -> Int
judge a = (\x -> if elem (-1) x then 0 else 1) $ map snd $ M.toList $ M.fromListWith (\x y -> if x == y then x else -1) a

getPremise :: Int -> [Int] -> [(Int, Int)]
getPremise n choise = union (zip ([0..(n-1)]\\choise) (repeat 0)) (zip (choise) (repeat 1))

main = do
 n <- read <$> getLine :: IO Int
 let choices = subsequences [0..(n-1)]
 statements <- replicateM n getInputData
 let ans1 = map length choices
 let ans2 = map judge $ zipWith (++) (map (getPremise n) choices) $ map (concat . (getHonestStatement statements [])) choices
 print $ maximum $ zipWith (*) ans1 ans2