Problem 2265. 2048 Next Move

Given a board in the game 2048 (see the game here: 2048) and a direction ('up','down','left', or 'right'), move the game forward one turn.

Move and merge blocks as required by the game's rules, but for simplicity do not insert a new 2.

Example 1

 board = [ ...
    0     0     0     2
    0     0     4     4
    0     0     0    16
    0     0     0    16]
 dir = 'up'
 newBoard = [ ...
    0     0     4     2
    0     0     0     4
    0     0     0    32
    0     0     0     0 ]

Example 2

 board = [ ...
    0     2   128     4
    0    16     4    32
    0     8     0     0
    0     0     2     0 ]
 dir = 'right'
 newBoard = [ ...
    0     2   128     4
    0    16     4    32
    0     0     0     8
    0     0     0     2 ]

Example 3. Resolving Ambiguity

If we think of the directions as defining the pull of gravity, then we resolve ambiguous cases by first merging the two "lowest" blocks. See below.

 board = [ ...
    0     4     4     4
    4     4     4     0
    2     2     2     2
    0     0     0     0 ]
 dir = 'left'
 newBoard = [ ...
    8     4     0     0
    8     4     0     0
    4     4     0     0
    0     0     0     0 ]

Inspired by a suggestion from Nick Howe.