Description

Input

The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 10^5$) — the number of strings.

Then $n$ lines follow, the $i$-th of which contains non-empty string $s_i$ of length at most $\mathbf{8}$, consisting of lowercase English letters. Among the given $n$ strings, there may be equal (duplicates).

The sum of $n$ over all test cases doesn't exceed $10^5$.

Output

For each test case, output a binary string of length $n$. The $i$-th bit should be $\texttt{1}$ if there exist two strings $s_j$ and $s_k$ where $s_i = s_j + s_k$, and $\texttt{0}$ otherwise. Note that $j$ can be equal to $k$.

Samples

3
5
abab
ab
abc
abacb
c
3
x
xx
xxx
8
codeforc
es
codes
cod
forc
forces
e
code

10100
011
10100101

Note

In the first test case, we have the following:

• $s_1 = s_2 + s_2$, since $\texttt{abab} = \texttt{ab} + \texttt{ab}$. Remember that $j$ can be equal to $k$.
• $s_2$ is not the concatenation of any two strings in the list.
• $s_3 = s_2 + s_5$, since $\texttt{abc} = \texttt{ab} + \texttt{c}$.
• $s_4$ is not the concatenation of any two strings in the list.
• $s_5$ is not the concatenation of any two strings in the list.

Since only $s_1$ and $s_3$ satisfy the conditions, only the first and third bits in the answer should be $\texttt{1}$, so the answer is $\texttt{10100}$.