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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local function check(x, vec)
  local w = {}
  for i = 1, #vec do
    w[i] = vec[i]
  end
  local isok = true
  for i = 1, 62 do
    local rmpos = 0
    for j = #w, 1, -1 do
      if w[j] % 2 == 1 then
        rmpos = j
        break
      end
    end
    if rmpos == 0 then
      if x % 2 == 1 then
        isok = false
        break
      end
    else
      local v = w[rmpos]
      table.remove(w, rmpos)
      if x % 2 == 1 then
        x = v ~ x
      end
      for j = 1, #w do
        if w[j] % 2 == 1 then
          w[j] = v ~ w[j]
        end
      end
    end
    x = x // 2
    for j = 1, #w do
      w[j] = w[j] // 2
    end
  end
  return isok
end
local q = io.read("*n")
for iq = 1, q do
  local n = io.read("*n", "*l")
  local as = io.read()
  local a = {}
  for ac in as:gmatch("%d+") do
    table.insert(a, tonumber(ac))
  end
  local s = io.read()
  local t = {}
  local valid = true
  for i = n, 1, -1 do
    if s:sub(i, i) == "0" then
      table.insert(t, a[i])
    else
      if not check(a[i], t) then
        valid = false break
      end
    end
  end
  print(valid and 0 or 1)
end