S1. Good Fours and Good Fives
레이팅 미적용의견: 0
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.
Marks
The following table shows how the available 15 marks are
distributed.
| Marks Awarded | Bounds on \(N\) | Additional Constraints |
|---|---|---|
| 3 marks | \(1 \leq N \leq 10\) | None |
| 2 marks | \(1 \leq N \leq 100\ 000\) | \(N\) is a multiple of \(4\) |
| 2 marks | \(1 \leq N \leq 100\ 000\) | \(N\) is a multiple of \(5\) |
| 8 marks | \(1 \le N \leq 1\ 000\ 000\) | None |
The input consists of one line containing a number \(N\).
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.
141This is one of the examples in the problem description.
403This is one of the examples in the problem description.
60There is no way to use a sum of fours and fives to get \(6\).
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S1. Good Fours and Good Fives
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S1. Good Fours and Good Fives