You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
You are given an array of $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$.

In one operation you split the array into two parts: a non-empty prefix and a non-empty suffix. The value of each part is the bitwise XOR of all elements in it. Next, discard the part with the smaller value. If both parts have equal values, you can choose which one to discard. Replace the array with the remaining part.

The operations are being performed until the length of the array becomes $$$1$$$. For each $$$i$$$ ($$$1 \le i \le n$$$), determine whether it is possible to achieve the state when only the $$$i$$$-th element (with respect to the original numbering) remains.

Formally, you have two numbers $$$l$$$ and $$$r$$$, initially $$$l = 1$$$ and $$$r = n$$$. The current state of the array is $$$[a_l, a_{l+1}, \ldots, a_r]$$$.

As long as $$$l < r$$$, you apply the following operation:

- Choose an arbitrary $$$k$$$ from the set $$$\{l, l + 1, \ldots, r - 1\}$$$. Denote $$$x = a_l \oplus a_{l + 1} \oplus \ldots \oplus a_k$$$ and $$$y = a_{k + 1} \oplus a_{k + 2} \oplus \ldots \oplus a_{r}$$$, where $$$\oplus$$$ denotes the bitwise XOR operation.
- If $$$x < y$$$, set $$$l = k + 1$$$.
- If $$$x > y$$$, set $$$r = k$$$.
- If $$$x = y$$$, either set $$$l = k + 1$$$, or set $$$r = k$$$.

For each $$$i$$$ ($$$1 \le i \le n$$$), determine whether it is possible to achieve $$$l = r = i$$$.

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10\,000$$$). The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 10\,000$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i < 2^{60}$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10\,000$$$.

## Output Format
For each test case, output a single string of length $$$n$$$ where the $$$i$$$-th element is equal to 1 if it is possible to achieve $$$l = r = i$$$ and is equal to 0 otherwise.

## Examples
```input
6
6
3 2 1 3 7 4
5
1 1 1 1 1
10
1 2 4 8 4 1 2 3 4 5
5
0 0 0 0 0
5
1 2 3 0 1
1
100500
```
```output
111111
10101
0001000000
11111
11001
1
```

## Note
In the first test case, it is possible to achieve $$$l = r = i$$$ for any $$$i$$$ from $$$1$$$ to $$$n$$$:

- for $$$i=1$$$: $$$[1; 6] \rightarrow [1; 4] \rightarrow [1; 1]$$$;
- for $$$i=2$$$: $$$[1; 6] \rightarrow [1; 3] \rightarrow [2; 3] \rightarrow [2; 2]$$$;
- for $$$i=3$$$: $$$[1; 6] \rightarrow [1; 3] \rightarrow [3; 3]$$$;
- for $$$i=4$$$: $$$[1; 6] \rightarrow [1; 4] \rightarrow [4; 4]$$$;
- for $$$i=5$$$: $$$[1; 6] \rightarrow [5; 6] \rightarrow [5; 5]$$$;
- for $$$i=6$$$: $$$[1; 6] \rightarrow [6; 6]$$$.

Let's take a closer look at $$$i = 2$$$. Initially $$$l = 1$$$, $$$r = 6$$$.

1. We can choose $$$k = 3$$$ and set $$$r = k = 3$$$ since $$$(3 \oplus 2 \oplus 1) = 0 \ge 0 = (3 \oplus 7 \oplus 4)$$$;
2. Next, we can choose $$$k = 1$$$ and set $$$l = k + 1 = 2$$$ since $$$3 \le 3 = (2 \oplus 1)$$$;
3. Finally, we can choose $$$k = 2$$$ and set $$$r = k = 2$$$ since $$$2 \ge 1$$$.

Now solve the problem and return the code.