Suppose we want to monitor how locks are used in our system. As the first step, we log moments of acquire and release for each lock in the following format:

• ACQUIRE X
• RELEASE X

where X is some integer ID (1 <= X <= 1,000,000) of the lock.

All locks must be released in the reverse order of acquiring them; for example, this is a correct event sequence:

1. ACQUIRE 364
2. ACQUIRE 84
3. RELEASE 84
4. ACQUIRE 1337
5. RELEASE 1337
6. RELEASE 364

The following sequence violates this rule because lock 84 is still acquired while releasing lock 364:

1. ACQUIRE 364
2. ACQUIRE 84
3. RELEASE 364
4. RELEASE 84

It's also dangerous to leave locks acquired after application termination, as other processes in the system may be blocked while waiting on them, so such a sequence is incorrect, too:

1. ACQUIRE 364
2. ACQUIRE 84
3. RELEASE 84

since lock 364 is never released.

Another problem is lock misuse: releasing a lock that was never acquired:

1. ACQUIRE 364
2. RELEASE 84
3. RELEASE 364

And it is also invalid to acquire an already acquired lock (usually resulting in a deadlock):

1. ACQUIRE 364
2. ACQUIRE 84
3. ACQUIRE 364
4. RELEASE 364

Task

Write a program that, given a list of N (0 <= N <= 1,000,000) lock acquire and release events (counting from 1), checks if there were any problems (acquire-release order violation, dangling acquired lock, acquiring a lock twice or releasing a free lock), and if so, tells the earliest time that could be detected.

You are given an array of strings where each string is either "ACQUIRE X" or "RELEASE X", where all Xs are integers in the range [1..1000000].

Return

• 0, if there were no lock-related problems even after program termination
• N + 1, if the only issue after program termination was dangling acquired locks
• K, in case event number K violated any of the principles (release a lock not acquired previously, acquire an already held lock OR violate lock acquire-release order)

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Count Palindromic Substrings

Problem Description

A string S is called a palindrome if it reads the same backward as forward. Any non-empty string has substrings that are palindromes. For example, for S = "hellolle", valid palindromic substrings include:

• "ellolle"
• "ll" — appears more than once at different positions
• "lol" and "lloll"
• and all single characters (8 of them in this example)

Write a function that, given a string S consisting of only lowercase English letters, counts how many different ways there are to pick a palindrome substring from S.

Input

• A string S (1 ≤ |S| ≤ 1000), consisting of lowercase English letters only.

Output

• An integer representing the total number of palindromic substrings (counting each distinct position, not just value).

Example

def count_palindromic_substrings(S):
    n = len(S)
    count = 0
    
    for center in range(2 * n - 1):
        l = center // 2
        r = l + (center % 2)
        while l >= 0 and r < n and S[l] == S[r]:
            count += 1
            l -= 1
            r += 1
    return count

# Example
print(count_palindromic_substrings("hellolle"))  # Output: total count of palindromic substrings

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Given a binary search implementation, write a verification program that:

• prints "CORRECT" if the binary search is implemented properly
• or prints a counter-example:
  • first line: number of elements in the array
  • second line: space-separated sorted array
  • third line: a target value for which the implementation returns an incorrect result

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