Problem
In the mystical realm of Computia, the Modulo Wizards have left behind a magical array encrypted by a 'modulo dance'. This enchanted sequence holds the key to unlocking secrets of immense power, and it's your quest to restore it to its original order. Each element in the array corresponds to a unique index, determined by a mysterious modulo value. Your task is to decipher this array using your knowledge of modular arithmetic. To begin, you'll receive an array of integers from standard input. Your mission is to rearrange these integers to their original order by leveraging the given modulo values. The challenge lies in understanding how each element's position is determined by the modulo operation. Steps to solve: 1. Identify the modulo value associated with each element to ascertain its original index. 2. Rearrange the elements based on these indices to restore the array to its intended order. 3. Consider edge cases, such as repeated numbers or negative values, which may affect the indexing.
- Consider using a data structure like a hash map to store the original indices for quick access.
- Think about how the modulo operation can map indices back to their original positions.
- Pay attention to edge cases, such as when all numbers are the same or when negative indexing might occur.
- For optimization, ensure that your solution can handle large arrays efficiently.
Input format
The first line contains an integer n (1 <= n <= 1000), the size of the array. The second line contains n integers a_i (0 <= a_i <= 1000), representing the elements of the array.
Output format
Output the array in its original order after undoing the modulo shuffle.
Constraints
1 <= n <= 1000, 0 <= a_i <= 1000
Sample input
5 5 9 2 7 4
Sample output
2 4 5 7 9