Double Strings
Description
You are given $n$ strings $s_1, s_2, \dots, s_n$ of length at most $\mathbf{8}$.
For each string $s_i$, determine if there exist two strings $s_j$ and $s_k$ such that $s_i = s_j + s_k$. That is, $s_i$ is the concatenation of $s_j$ and $s_k$. Note that $j$ can be equal to $k$.
Recall that the concatenation of strings $s$ and $t$ is $s + t = s_1 s_2 \dots s_p t_1 t_2 \dots t_q$, where $p$ and $q$ are the lengths of strings $s$ and $t$ respectively. For example, concatenation of "code" and "forces" is "codeforces".
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 $10^5$.
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 $k$.
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.