Design a data stream processor that maintains a sliding window of the last N elements and can answer queries about the most frequent element in the current window and elements that appear exactly twice in the current window.

The processor receives a stream of operations. Elements are added to the window, and queries can be made on the current contents of the window.

The supported operations are:

• ADD element – Add an element to the current window. If the window size exceeds N, remove the oldest element from the window.
• MOST_FREQUENT – Return the element with the highest frequency in the current window. If multiple elements have the same frequency, return the lexicographically smallest element.
• EXACTLY_TWICE – Return all elements that appear exactly twice in the current window, sorted lexicographically.

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Example 1

Input

4
9
ADD A
ADD B
ADD A
MOST_FREQUENT
EXACTLY_TWICE
ADD C
ADD A
MOST_FREQUENT
EXACTLY_TWICE

Output

A
A
A
A C

Explanation

After adding A, B, and A, the current window is:

[A, B, A]

The element A appears twice, making it the most frequent element and the only element that appears exactly twice.

After adding C and then A, the window shifts and the oldest elements are removed. The current window becomes:

[A, C, A, C]

The most frequent elements and the elements appearing exactly twice are both A and C. Since A is lexicographically smaller, the MOST_FREQUENT query returns A, while EXACTLY_TWICE returns:

A C

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Input Format

• Line 1: Integer N — the size of the sliding window.

• Line 2: Integer Q — the number of operations.

• The next Q lines each contain one operation:

  • ADD x
  • MOST_FREQUENT
  • EXACTLY_TWICE

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Output Format

Return a string array containing the outputs of all query operations (MOST_FREQUENT and EXACTLY_TWICE) in the order they appear.

For EXACTLY_TWICE, output all qualifying strings in lexicographical order separated by a single space.

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Constraints

• 1 ≤ N ≤ 100000
• 1 ≤ Q ≤ 200000
• 1 ≤ length(element) ≤ 20
• Elements contain English letters only.
• The total number of characters in the expected output will not exceed 10^6.

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Sample Case 0

Sample Input 0

4
9
ADD A
ADD B
ADD A
MOST_FREQUENT
EXACTLY_TWICE
ADD C
ADD A
MOST_FREQUENT
EXACTLY_TWICE

Sample Output 0

A
A
A
A C

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Function Signature

vector<string> processOperations(int window_size, vector<string> operations)

Return

Return a vector<string> containing the answers to all query operations in the order they occur.