Inventory Management System

You are given an inventory management system that can store at most \(N\) distinct items. Each item has a name and a quantity. You need to implement commands to add or remove items from the inventory.

When adding an item:

• If the item already exists, increase its quantity by the given amount.
• If the item does not exist and the inventory has not reached its maximum distinct item capacity \(N\), add the item with the given quantity.
• If the inventory is full (i.e. it already contains \(N\) distinct items), ignore the add command.

When removing an item:

• If the item exists, reduce its quantity by the given amount. If the removal amount is greater than or equal to the current quantity, remove the item entirely from the inventory.
• If the item does not exist, ignore the command.

After processing each command, output the current state of the inventory. The inventory should be sorted lexicographically by item name.

Note: Input is read from stdin and output is printed on stdout. Each line of output corresponds to the inventory state after processing each command. Each item in the inventory is printed in the format item:quantity and items are separated by a single space. If the inventory is empty, print EMPTY.

inputFormat

The first line contains a positive integer \(N\) (maximum distinct items in the inventory).

The second line contains a positive integer \(M\), denoting the number of commands.

The following \(M\) lines each contain a command in one of the following formats:

• ADD item_name quantity
• REMOVE item_name quantity

All tokens in a command are separated by space. The quantity is a positive integer.

outputFormat

For each command, output one line representing the current inventory state after processing that command. The inventory should be printed as a list of items sorted lexicographically by item name. Each item must be printed in the format item:quantity and separated by a single space. If the inventory is empty, output EMPTY.

## sample

5
5
ADD potion 5
ADD sword 3
REMOVE potion 2
ADD shield 4
REMOVE sword 3

potion:5
potion:5 sword:3
potion:3 sword:3
potion:3 shield:4 sword:3
potion:3 shield:4

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