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In datastruct class, the teacher gives partychen a simple sort question:
A permutation $p[0]$, $p[1]$, …, $p[n-1]$ is a sequence containing each number from $0$ to $n-1$ exactly once. The result of applying permutation $p$ to an array $A$ of length $n$ is an array $B$ of length $n$, where $B[p[i]] = A[i]$ (0-based indices).
Given an array $A$, find a permutation which has the effect of sorting the elements of $A$ in non-descending order, i.e., an order where each element is greater than or equal to the previous one. If there are several suitable permutations output the lexicographically smallest one.
The permutation $p[0]$, $p[1]$, …, $p[n-1]$ is considered lexicographically smaller than the permutation $q[0]$, $q[1]$, …, $q[n-1]$ if there is an index $i$ such that $p[i] < q[i]$ and the equation $p[j] = q[j]$ holds for all $j < i$.
The first line of input gives the number of cases, $N$($1 \leq N \leq 100$). $N$ test cases follow.
In each test case, there are two lines. The first line is a interger $M$($1 \leq M \leq 10000$), representing the numbers of array $A$, and in the second line there are $M$ intergers.
Output the permutation $p$ as discrible above.
2 3 2 3 1 4 2 1 3 1
1 2 0 2 0 3 1
In case 1: The element that is originally at position $0$ goes to position $1$. The elements originally at positions $1$ and $2$ go to positions $2$ and $0$, respectively.
In case 2: There are two suitable permutations: ${2, 0, 3, 1}$ and ${2, 1, 3, 0}$. The first one is lexicographically smaller.