Problem:
Score : 400 points

Problem Statement

There are two persons, numbered 0 and 1, and a variable x whose initial value is 0.
The two persons now play a game.
The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):

Person S_i does one of the following:

Replace x with x \oplus A_i, where \oplus represents bitwise XOR.

Do nothing.

Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.

Determine whether x becomes 0 at the end of the game when the two persons play optimally.

Solve T test cases for each input file.

Constraints

1 \leq T \leq 100

1 \leq N \leq 200

1 \leq A_i \leq 10^{18}

S is a string of length N consisting of 0 and 1.

All numbers in input are integers.

Input

Input is given from Standard Input in the following format.
The first line is as follows:

T

Then, T test cases follow.
Each test case is given in the following format:

N
A_1 A_2 \cdots A_N
S

Output

For each test case, print a line containing 0 if x becomes 0 at the end of the game, and 1 otherwise.

Sample Input 1

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000

Sample Output 1

1
0
0

In the first test case, if Person 1 replaces x with 0 \oplus 1=1, we surely have x \neq 0 at the end of the game, regardless of the choice of Person 0.

In the second test case, regardless of the choice of Person 1, Person 0 can make x=0 with a suitable choice.

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import qualified Data.ByteString.Char8 as B
import           Data.Maybe (fromJust)
import           Control.Monad.State.Strict
import qualified Data.Set as S
import           Data.Bits (xor)

main :: IO ()
main = do
  t <- getInt
  replicateM_ t testCase

testCase :: IO ()
testCase = do
  n <- getInt
  as <- reverse . fmap (fst . fromJust . B.readInt) . B.words <$> B.getLine
  s <- reverse <$> getLine
  putStrLn
    $ if solve s as (S.singleton 0)
      then "0"
      else "1"

solve _ _ e
  | null e = False
solve "0" [h] acc = 0 `elem` acc || 0 `xor` h `elem` acc
solve "1" [h] acc = 0 `elem` acc && 0 `xor` h `elem` acc
solve ('0':rest) (h:t) acc = let s = acc `S.union` (S.map (`xor` h) acc)
                             in solve rest t s
solve ('1':rest) (h:t) acc = let s = S.filter (\n -> n `xor` h `elem` acc) acc
                             in solve rest t s

getInt = fst . fromJust . B.readInt <$> B.getLine