Majority Element Finder

Given an integer array of size \( n \), determine which elements, if any, appear more than \( \lfloor n/2 \rfloor \) times. In other words, find the element(s) whose count is strictly greater than \( n/2 \). If such element exists, output all of them in ascending order (separated by a space). Otherwise, output None. Note that while typically only one element can satisfy this condition, your solution should be capable of handling multiple valid elements if they occur.

Example:

• For \( n = 7 \) and the array [3, 3, 4, 2, 4, 4, 4], the output should be 4 because 4 appears 4 times which is more than \( \lfloor 7/2 \rfloor = 3 \).
• For \( n = 5 \) and the array [3, 1, 3, 2, 4], there is no element appearing more than \( \lfloor 5/2 \rfloor = 2 \) times; hence, the output is None.

inputFormat

The input is read from stdin and consists of two lines:

1. The first line contains a single integer \( n \) representing the number of elements in the array.
2. The second line contains \( n \) space-separated integers.

If \( n = 0 \), the second line will be empty.

outputFormat

The output should be printed to stdout as follows:

• If one or more majority elements are found, print them in ascending order separated by a single space.
• If no majority element exists, print None (without quotes).

## sample

7
3 3 4 2 4 4 4

4

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