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Bad Tuples CodeChef Solution

Bad Tuples CodeChef Solution

Problem

A tuple of positive integers (a, b, c) is said to be a bad tuple if a, b, c are distinct, a divides b, and b divides c. For example, (1, 2, 4) and (7, 21, 42) are bad tuples while (1, 2, 3) and (2, 4, 4) are not.

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Chef has the¬†N¬†integers from¬†1¬†to¬†N¬†with him. He wants to pick a¬†subset¬†of these numbers such that it doesn’t contain a¬†bad tuple. How many distinct subsets can he pick?

Input Format

  • The first and only line of input contains a single integer¬†N, the number of available integers.

Output Format

Output the number of subsets that don’t contain any bad tuples in them.

Constraints

  • 1 \leq N \leq 60

Sample 1:

Input

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Output

2
4

Sample 2:

Input

Output

4
14

Explanation:

Test case¬†1:¬†There are¬†4¬†subsets in total ‚ÄĒ¬†\{\},¬†\{1\},¬†\{2\},¬†\{1, 2\}. None of these subsets violate the condition.

Test case¬†2:¬†There are¬†16¬†subsets in total, out of which¬†2¬†subsets ‚ÄĒ¬†\{1, 2, 4\}¬†and¬†\{1, 2, 3, 4\}¬†‚ÄĒ violate the given condition as they contain the bad tuple¬†(1, 2, 4)¬†in them.

SOLUTION

Bad Tuples CodeChef Solution

SOLUTION

Bad Tuples CodeChef Solution

SOLUTION

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