CCC '22 S1 - Good Fours and Good Fives

Canadian Computing Competition: 2022 Stage 1, Senior #1

Finn loves Fours and Fives. In fact, he loves them so much that he wants to know the number of ways a number can be formed by using a sum of fours and fives, where the order of the fours and fives does not matter. If Finn wants to form the number $14$, there is one way to do this which is $14 = 4 + 5 + 5$. As another example, if Finn wants to form the number $20$, this can be done two ways, which are $20 = 4 + 4 + 4 + 4 + 4$ and $20 = 5 + 5 + 5 + 5$. As a final example, Finn can form the number $40$ in three ways: $40 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4$, $40 = 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5$, and $40 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5$.

Your task is to help Finn determine the number of ways that a number can be written as a sum of fours and fives.

Input Specification

The input consists of one line containing a number $N$.

The following table shows how the available $15$ marks are distributed.

Output Specification

Output the number of unordered sums of fours and fives which form the number $N$. Output $0$ if there are no such sums of fours and fives.

Sample Input 1

Sample Output 1

Explanation

This is one of the examples in the problem description.

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Sample Input 2

Sample Output 2

Explanation

This is one of the examples in the problem description.

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Sample Input 3

Sample Output 3

Explanation

There is no way to use a sum of fours and fives to get $6$.