Write a Python program to solve the popular "Hashiwokakero" or "Bridges" puzzle. The input to your program will be a rectangular array of numbers and dots, for example:

$\mathrm{.}1..\mathrm{.}6..\mathrm{.}7...\mathrm{.}4\mathrm{.}4\mathrm{.}2.$

$.\mathrm{.}4\mathrm{.}2.\mathrm{.}2..\mathrm{.}3\mathrm{.}8..\mathrm{.}6\mathrm{.}2$

$....\mathrm{.}2..............$

$5.$c$\mathrm{.}7..$a$.$a$.\mathrm{.}5\mathrm{.}6.\mathrm{.}8\mathrm{.}5$

$............\mathrm{.}2......$

$..\mathrm{.}5..\mathrm{.}9.$a$.\mathrm{.}8.$b$\mathrm{.}8\mathrm{.}4.$

$4\mathrm{.}5...............\mathrm{.}3$

$...\mathrm{.}2.\mathrm{.}4.\mathrm{.}1\mathrm{.}5..\mathrm{.}2...$

$\mathrm{.}2\mathrm{.}7\mathrm{.}4..\mathrm{.}7\mathrm{.}2.\mathrm{.}5..\mathrm{.}3.$

$...........\mathrm{.}4.\mathrm{.}3\mathrm{.}1\mathrm{.}2$

Each number represents an "island", while the dots represent the empty space $($water$)$ between the islands. Numbers larger than $9$ are indicated by $\text{'}$a$\text{'}(10),\text{'}$b$\text{'}(11)$ or $\text{'}$c$\text{'}(12).$ The aim is to connect all the islands with a network of bridges, satisfying these rules:

$-$all bridges must run horizontally or vertically

$-$bridges are not allowed to cross each other, or other islands

$-$there can be no more than three bridges connecting any pair of islands

$-$the total number of bridges connected to each island must be equal to the number on the island

For example, after reading the $10-$line input above, your program might produce the attached out $($see image below$).$

Note that single bridges are indicated by the characters $\text{'}-\text{'}$ or $\text{'}|\text{'},$ pairs of bridges by $\text{'}=\text{'}$ or $\text{'}"\text{'}$ and triples by $\text{'}$E$\text{'}$ or $\text{'}$#$\text{'},$ depending on whether they run horizontally or vertically. Water between bridges and islands is indicated by space characters $\text{'}\text{'}.$

In some cases, there may be many solutions, in which case your program should only print one solution.