Phone storage used and free

Problem

A phone has a fixed total storage in GB. Installing an app needs enough free space, and removing more than is used is impossible.

Write a class Smartphone with private totalStorage and storageUsed, boolean install(int gb), boolean remove(int gb) and two getters that are worked out from the fields: getAvailable() and getUsagePercent(). Sizes of 0 or less are invalid.

Input, output and limits

Input: The first line has the total storage. The second line has q. Each of the next q lines is install x or remove x.
Output: After a successful command: FREE f GB, p% USED, with p printed with one digit after the decimal point. Otherwise INVALID SIZE, NOT ENOUGH SPACE, FREE f GB or CANNOT REMOVE MORE THAN USED.
Constraints: 1 ≤ total ≤ 1024
1 ≤ q ≤ 1000
-10^4 ≤ x ≤ 10^4

Examples

Example

Input

64
3
install 40
install 30
remove 10

Output

FREE 24 GB, 62.5% USED
NOT ENOUGH SPACE, FREE 24 GB
FREE 34 GB, 46.9% USED

Only 24 GB is free, so the 30 GB app does not fit.

Hints

Try the problem first. Open one hint at a time.

Hint 1

Do not store available as a field: work it out as totalStorage - storageUsed, so it can never be out of date.

Hint 2

Use 100.0 in the percentage so the division keeps its decimals.

Hint 3

Print %% inside printf to show a % sign.

Write your Java code, run it on the examples and submit it to hidden tests.

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