You want to throw a party and a few of your friends are willing to help at the bar for a part of the night. For example

• Carine wants to help between 22:00 and 23:00
• Dina between 23:30 and 1:00
• Erik between 21:00 and 22:30
• Frank between 23:05 and 23:25
• …

Design an efficient algorithm that, given a list of hours with people who want to help, checks if there is someone in the bar at every point between a given start time and end time.

Assignment

Write a Python function party(intervals: list, start: int, end: int) that checks if there are enough helpers between the given start time and end time.

A tuple with 2 elements (start_time, end_time) is used to model a time interval. Timestamps are represented as simple integers. Note: The start time is inclusive, but the end time is exclusive.

Examples

>>> party([(592, 628), (646, 700), (556, 610), (631, 643)], 592, 700)
False
>>> party([(592, 628), (646, 700), (556, 610), (592, 646)], 592, 700)
True
>>> party([(100, 101)], 100, 101)
True
>>> party([], 100, 101)
False
>>> party([], 100, 100)
True