Write a program which finds solution to the following $3$ hierarchically organized constraint satisfaction problems, involving $13$ variables $\{$A$,$ B$,$ C$,...,$ M$\}$ which can take integer values in $\{1,...,120\}$; solutions can use the same integer for different variables.

a$.$ Problem A: Find a solution to the constraint satisfaction problem involving the six variables A$,$ B$,$ C$,$ D$,$ E and F and constraints C$1,...,$ C$5$:

$($C$1)$ A$=$B$**2$ C$**2$

$($C$2)$ E$+$F$>$B

$($C$3)$ D$=$B$**2-3*$A

$($C$4)($B$-$C$)**2=$E$*$F$*$C$-1861$

$($C$5)$ C$+$D$+$E$+$F$<120$

b$.$ Problem B: Find a solution to the constraint satisfaction problem involving ten variables A$,...,$ J which satisfy constrains C$1,...,$ C$12$:

$($C$6)($G$+$I$)**3=($H$-$A$-1)**2$

$($C$7)$ B$*$E$*$F$=$H$*$B$-200$

$($C$8)($C$+$I$)**2=$B$*$E$*($G$+1)$

$($C$9)$ G$+$I$180$

$($C$11)$ J $<$ H$-$C$-$G

$($C$12)$ J $>$ B$*$G$+$D$+$E$+$G

c$.$ Problem C: Find a solution to the constraint satisfaction problem involving $13$ variables A$,...,$ M which satisfy constrains C$1,...,$ C$17$:

$($C$13)$ K$*$L$*$M$=$B$*($B$+5)$

$($C$14)$ F$**3=$K$*$K$*$M$*$M$*10+331$

$($C$15)$ H$*$M$*$M$=$J$*$K$-20$

$($C$16)$ J$+$L$=$I$*$L

$($C$17)$ A$+$D$+$M$=$B$*($F$-2)$

Remark: In the above equations the letter $$I$$ was put into bold face to avoid being mistaken as the number $1.$ Moreover, the letter $$J$$ looks somewhat similar to the letter $$I$$ but to better distinguish the two letters $$J$$ is never in bold face.

Your program should contain a counter nva $($number of variable assignments$)$ that counts the number of times an initial integer value is assigned to a variable or the assigned integer to the particular variable is changed; in addition to outputting the solution to the CSV also report the value of this variable at the end of the run, and develop an interface to call your program for CSP Problems A$,$ B$,$ or C$.$ Your program should return a solution or $$no solution exists$$ and the value of nva after the program terminates. Moreover, terminate the search as soon as you found a solution$$do not search for additional solutions.