What is n, Daddy?

Interview

Time limit2sMemory limit512 MB

Summary

Count the ordered pairs (a, b) with 1 <= b <= a <= 5 and possibly a single hand, summing to n.

Level: Easy2 of 10
Topics: Math, Brute force, Implementation, Combinatorics
Solved: No attempts yet

Problem

Natalie is learning to count on her fingers. When her Daddy tells her a number $n$ ( $1 \le n \le 10$ ), she asks "What is $n$ , Daddy?", meaning "How many fingers should I hold up on each hand so that the total is $n$ ?"

Each hand can hold up at most 5 fingers. Her Daddy gives the correct finger representations according to the following rules:

the number may be represented on one hand or on two hands;
if the number is represented on two hands, each hand holds up at least one finger, and the larger number is given first.

For example, if Natalie asks "What is 4, Daddy?", her Daddy may reply:

4 is 4.
4 is 3 and 1.
4 is 2 and 2.

Your job is to count how many different answers Daddy can give.

Input

The input consists of a single integer $n$ with $1 \le n \le 10$ .

Output

Output the number of ways to represent $n$ with the fingers, following the rules above.

Examples1

Example 1
Input
```
4
```
Expected output
```
3
```