The Goal

Make more than 10,000 points.

Rules

Players take turns.
The player receives 6 dice.

The player may choose to pass and score the points, or re-roll the dice.
To re-roll the dice, the player must keep at least one of the dice.
If a dice roll fails to score points, all accumulated points are lost.

Each 1 is worth 100 points and each 5 is worth 50 points. A three of a kind is worth 100 times the value of the number on the dice, except in the case of a three of 1s, which is worth 1,000 points.

A 5 is worth 50 points
A 1 is worth 100 points
Three 2s are worth 200 points
Three 3s are worth 300 points
Three 4s are worth 400 points
Three 5 are worth 500 points
Three 6 are worth 600 points
Three 1's worth 1,000 points

Four of a kind (four dice of the same value), five of a kind (five dice of the same value) and six of a kind (six dice of the same value) are incremented by the value of the corresponding three of a kind. For example, a three of 2 is worth 200 points, a four of 2 is worth 400, a five of 2 is worth 600 and a six of 2 is worth 800.

A sequence of 1, 2, 3, 4, 5 and 6 is worth 1,500 points.

For a combination to count, it must be obtained in a single throw.

Example

First roll of the dice : Player receives 6 dice with values 1 4 1 1 3 6
Player keeps three dice of 1 for a score of 1000 points providing to the standard output one line with 1 1 1

Second roll of the dice : Player receives 3 dice with values 2 5 1
Player passes for a score of 150 points and scores a total of 1000 + 150 = 1150 points providing to the standard output one line with pass

Note

Warning: one turn allows the dice to be re-rolled a maximum of 2 times.

Victory conditions

Be the first to reach 10,000 points.

Defeat conditions

Your opponent reaches 10,000 points before you do.
Your code does not respond in time or returns an unrecognized command.

Game Input

Input

Line 1: an integer count, the number of rolled dice

Line 2: a string of space-separated integer values, the values of rolled dice

Output

A single line containing pass or a list of kept dice as a string of integers separated by spaces such as 1 1 5.