Black Box

문제

The following Python-like pseudo code for function BlackBox() takes a list of positive integers and shuffles the integers in the list in a specific way, and returns the result as a list.

Three list methods are used below; For a list L, len(L) returns the number of items in L. L.append(x) adds the item x to the end of L. L.pop(idx) removes the item at the specified index idx from the list L and returns the removed item.

Given a list Z of positive integers, write a program to reconstruct a list I such that Z = BlackBox(I).

function BlackBox( Banana ):
    if len( Banana ) ≤ 4 :
        exit("Too small Banana")
    Apple = [] # [] is an empty list
    Mango = 0
    Papaya = len( Banana )

    while( Papaya >= 2 ) :
        Kiwi = Banana[ Mango ]
        Apple.append( Kiwi )
        Banana.pop( Mango )
        Papaya = Papaya - 1
        Mango = ( Kiwi + Mango - 1 ) % Papaya
    # end of while

    Apple.append( Banana[ 0 ] )
    Pear = len( Apple ) - 1
    Orange = Apple[ Pear ]
    Lime = Apple[ 0 ]
    Coconut = Orange % Pear
    Melon = Apple[ Coconut ]
    Apple[ 0 ] = Melon
    Apple[ Coconut ] = Lime

    return ( Apple )
# end of function BlackBox

입력

Your program is to read from standard input. The first line contains a positive integer $nn$ representing the number of positive integers of a list Z, where 5 ≤ n ≤ 200\,000. The following $nn$ lines contain $nn$ positive integers of the list Z returned from BlackBox(I); the $ii$-th line contains the $ii$-th integer of the list Z between $11$ and $100000100\backslash ,000$, both inclusive.

출력

Your program is to write to standard output. Print $nn$ integers of the list I where Z = BlackBox(I), one per line; the $ii$-th line should contain the $ii$-th integer of I.

13
113
49
68
91
10
179
2
71
78
45
57
10
88

10
113
179
68
57
45
10
2
88
71
49
78
91

9
6
8
7
9
5
1
2
4
3

9
8
7
6
5
1
2
3
4