# UVa 11215 - How Many Numbers

## Problem

You might have heard the game of 24: given 4 integers, you’re to make an expression to get the number 24. For example, given 4, 4, 10, 10, you can write (1010-4)/4=24, given 1, 5, 5, 5, you can write (5-1/5)5=24.

In this problem, your task is a little bit harder: count the number of numbers that can be made. Don’t forget to count negative numbers and non-integers. You can use binary additions, subtractions, multiplications and divisions with parenthesis (unary operations are not allowed). Numbers cannot be concatenated to form a larger number (e.g. you cannot concatenate 1 and 2 to get 12).

For example, given two 1’s, exactly 3 numbers can be made: 1+1=2, 1-1=0, 1*1=1. You cannot get 11 or -1.

## Input

The input consists of at most 30 test cases. Each case begins with a line containing a single integer n (1 < n < 7), the number of integers given. The next line contains n non-negative integers not greater than 10. The last case is followed by a single zero, which should not be processed.

## Output

For each test case, print the case number and the number of numbers that can be made.

## Solution

`[l, r] = [l, k](+-*/)[k+1, r]`