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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

function solve(n, x, A, S, dp) {
  // console.log('n:', n, 'x:', x, 'a:', A[S.length - n], 's:', S[S.length - n])
  if (n === 0) return x === 0
  const s = S[S.length - n]
  if (dp[n] && dp[n][x]) {
    // console.log('exists:', n, x, dp[n][x])
    return dp[n][x]
  }

  let r
  if (s === '1') {
    // console.log('exec 1 do:')
    const r1 = solve(n - 1, x ^ A[S.length - n], A, S, dp)
    // console.log('exec 1 rm:')
    const r2 = solve(n - 1, x, A, S, dp)
    // console.log(r1, r2)
    r = r1 && r2
  } else {
    // console.log('exec 0:')
    r = solve(n - 1, x ^ A[S.length - n], A, S, dp) || solve(n - 1, x, A, S, dp)
  }
  if (!dp[n]) {
    dp[n] = {}
  }
  dp[n][x] = r
  return r
}

function main(input) {
  const inputs = input.split('\n')
  const T = Number(inputs[0])
  for(let i = 0; i < T * 3; i+=3) {
    const N = inputs[i + 1]
    const A = inputs[i + 2].split(' ')
    const S = inputs[i + 3]
    const r = solve(N, 0, A, S, {})
    console.log(r ? '0' : '1')
  }
  // console.log('n:', count)
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));