Find Combination Sequence

You are given two sequences of strings. The first sequence represents a list of ingredients and the second sequence represents the final dish obtained by combining these ingredients in a specific alternating order. In this process, the combination is done by picking ingredients alternately from the beginning and the end of the remaining list. Formally, if there are n ingredients, then for every index i (0-indexed):

• If i is even, then the ingredient from the front (at index \(\lfloor i/2 \rfloor\)) is chosen.
• If i is odd, then the ingredient from the back (at index \(n - \lceil i/2 \rceil\)) is chosen.

Your task is to determine and print the sequence of original indices (0-indexed) from the ingredients list that corresponds to the final dish order.

Note: The input guarantees that the final dish is always a valid result of this alternating picking process.

inputFormat

The input is read from stdin and has the following format:

n
ingredient1 ingredient2 ... ingredientn
final_dish1 final_dish2 ... final_dishn

where n is the number of ingredients (an integer), the second line contains n space-separated strings representing the ingredients in their original order, and the third line contains n space-separated strings representing the ingredients in the final dish order.

outputFormat

Output to stdout a single line containing n space-separated integers representing the 0-indexed positions of the ingredients used to create the final dish following the alternating process.

For example, if the output is:

0 3 1 2

then it indicates that the order of indices used was 0, 3, 1, and 2 respectively.

## sample

4
apple banana cherry date
apple date banana cherry

0 3 1 2

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