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As a unicorn, the ability of using magic is the distinguishing feature among other kind of pony. Being familiar with composition and decomposition is the fundamental course for a young unicorn. Twilight Sparkle is interested in the decomposition of permutations. A permutation of a set S = {1, 2, ..., n} is a bijection from S to itself. In the great magician 〞〞 Cauchy's two-line notation, one lists the elements of set S in the first row, and then for each element, writes its image under the permutation below it in the second row. For instance, a permutation of set {1, 2, 3, 4, 5} 考 can be written as:
\[\sigma = \begin{pmatrix}
1 & 2 & 3 & 4 & 5\\
2 & 5 & 4 & 3 & 1
\end{pmatrix}\]
Here 考(1) = 2, 考(2) = 5, 考(3) = 4, 考(4) = 3, and 考(5) = 1.
Twilight Sparkle is going to decompose the permutation into some disjoint cycles. For instance, the above permutation can be rewritten as:
\[\begin{pmatrix}
1 & 2 & 3 & 4 & 5\\
2 & 5 & 4 & 3 & 1
\end{pmatrix} = (1 \quad 2 \quad 5) (3 \quad 4)\]
Help Twilight Sparkle find the [b]lexicographic smallest solution. (Only considering numbers).[/b]
Input
Input contains multiple test cases (less than 10). For each test case, the first line contains one number n (1\(\leq\)n\(\leq\)\(10^5\)). The second line contains n numbers which the i-th of them(start from 1) is 考(i).
