Priority Queue Operations

You are required to implement a priority queue using a binary heap that supports three primary operations:

• INSERT <item> <priority>: Insert an element named item with an integer priority into the queue. If the item already exists, update its priority by replacing the old value.
• EXTRACT: Remove and print the item with the highest priority. In case of a tie, the item that was inserted earlier (i.e. with a smaller insertion order counter) is considered to have higher precedence. If the queue is empty, print error.
• INCREASE <item> <new_priority>: Increase the priority of the given item to new_priority only if new_priority is greater than the current priority. If the specified item does not exist in the queue, print error. If the new priority is not higher, do nothing.

You will receive the commands as input from stdin and should output responses to stdout. Only the EXTRACT operations (and error messages from failed operations) produce output.

Note: It is guaranteed that the number of commands is a positive integer. Use efficient methods to ensure your implementation passes within time limits.

inputFormat

The first line contains an integer Q representing the number of commands. Each of the next Q lines contains one command in one of the following formats:

• INSERT <item> <priority>
• EXTRACT
• INCREASE <item> <new_priority>

Items are strings without spaces and priorities are integers.

outputFormat

For each EXTRACT command, output a line containing the extracted item. Additionally, if an EXTRACT command is issued when the queue is empty or an INCREASE command is attempted on a non-existent item, output a line with error.

## sample

7
INSERT apple 3
INSERT banana 2
INSERT cherry 5
EXTRACT
INCREASE banana 6
EXTRACT
EXTRACT

cherry
banana
apple

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