Now, all the defragmenter needs to know is the number of regions. A region is a group of used squares that are all adjacent, not including diagonals. Every used square is in exactly one region: lone used squares form their own isolated regions, while several adjacent squares all count as a single region.

In the example above, the following nine regions are visible, each marked with a distinct digit:

11.2.3..--> .1.2.3.4
....5.6.
7.8.55.9
.88.5...
88..5..8
.8...8..
88.8.88.--> | |
V V
Of particular interest is the region marked 8; while it does not appear contiguous in this small view, all of the squares marked 8 are connected when considering the whole 128x128 grid. In total, in this example, 1242 regions are present.

How many regions are present given your key string?