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문제

This is the last problem of this contest, so Rikka doesn't want to add a lengthy background to it. Let us make all the things simple and clear.

You have a string $s$ of length $n$ which only contains lowercase English letters from "a" to "l" (there are $12$ possible letters). You can choose a permutation of these $12$ letters $p_{\texttt{a}}, p_{\texttt{b}}, \ldots, p_{\texttt{l}}$, and then consider the string $t = p_{s_1} p_{s_2} \ldots p_{s_n}$. Your task is to check for each $i$ from $1$ to $n$ whether the $i$-th suffix (the substring $t[i, n]$) can become the largest suffix of $t$ in lexicographical order after such modification.

입력

The first line contains a single integer $t$ ($1 \leq t \leq 10^3$), the number of test cases.

Each test case is given on a separate line containing a string $s$ ($1 \leq |s| \leq 10^5$, the string contains only lowercase English letters from "a" to "l").

It is guaranteed that there are at most $15$ test cases with $|s| > 10^3$.

출력

For each test case, output a single line with a binary string of length $|s|$. If the $i$-th suffix can become the largest one, the $i$-th position must contain "1". Otherwise, it must contain "0".

예제 입력 1

3
abaab
abcdefghijkllkjihgfedcba
aabbcccbaabcca

예제 출력 1

01100
111111111111011111111110
10101000100000