Counting Multiples Game

In this problem, Blue and his friends are playing a counting game. Since the year is \(2024\), they decide to take turns in ascending order reciting the positive integers which are multiples of \(20\) or \(24\). The first 10 numbers recited are: \(20, 24, 40, 48, 60, 72, 80, 96, 100, 120\).

Your task is to determine the \(n\)th number in this sequence, where \(n = 202420242024\). This is a result-filling problem; you only need to compute the result and submit it. When submitting your answer, output only this integer. Any extra output will result in no score.

Hint: A number is counted if it is divisible by \(20\) or \(24\). Note that numbers which are multiples of both (i.e. multiples of \(\text{lcm}(20,24)=120\)) should be counted only once.

inputFormat

There is no input for this problem.

outputFormat

Output a single integer, which is the \(202420242024\)th number in the sequence of positive integers that are multiples of \(20\) or \(24\).

sample

2429042904288