Practice Time with the exercise "Timer for Clash of Code"

Statement

Goal

You have to implement a version of the timer in Clash of Code. The timer starts at 5:00 and runs towards 0:00. The timer stop time changes based on players joining.

Here are the rules:
* Every time a player joins the clash, the timer stop time is set to

t - 256 / ( 2^(p - 1) )

where t is current time in seconds and p is the number of players in the room before the new player joined.
* If the result is under 0:00, set it to 0:00.
* If a player joins at the same time the game is supposed to start, set the new timer stop time instead of starting the game.

For example:

At 5:00 the timer starts, and there is one player (the one who started the clash).
At 4:47 the second player joins -> set to start 256 seconds from now, at 0:31.
At 3:56 the third player joins -> set to start 128 seconds from now, at 1:48.
At 3:13 the fourth player joins -> set to start 64 seconds from now, at 2:09.
At 2:09, the game starts.

Output: 2:09

The game starts if:
* The timer reaches the time it is set to stop at, or
* The timer reaches zero and there is more than one player, or
* The clash room is filled (8 players in total, 7 have joined).

Input

First line: An integer n for the number of players who join the clash

The next n lines: Time stamps in the format m:ss (minutes and seconds) at which a player joins the clash

Output

Output the time stamp at which the game starts in the format m:ss.
If no one joined, output NO GAME.

Constraints

n: Between 0 inclusive and 7 inclusive
Time stamps: Between 0:00 exclusive and 5:00 exclusive

The time stamps in the input are always in the right order (no invalid inputs).

Example

Input

1
4:47

Output

0:31

Solve it

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