Write a C$++$ program for the following algorithm

RobotCoinCollection$($C$[1..$n$,1..$m$])$

$//$Applies dynamic programming to compute the largest number of

$//$coins a robot can collect on an n $\backslash$times m board by starting at $(1,1)$

$//$and moving right and down from upper left to down right corner

$//$Input: Matrix C$[1..$n$,1..$m$]$ whose elements are equal to $1$ and $0$

$//$for cells with and without a coin, respectively

$//$Output: Largest number of coins the robot can bring to cell $($n$,$ m$)$

F$[1,1]$ C$[1,1]$; for j $2$ to m do F$[1,$ j $]$ F$[1,$ j $1]+$ C$[1,$ j $]$

for i $2$ to n do

F$[$i$,1]$ F$[$i $1,1]+$ C$[$i$,1]$

for j $2$ to m do

F$[$i$,$ j $]$ max$($F$[$i $1,$ j $],$ F$[$i$,$ j $1])+$ C$[$i$,$ j $]$

return F$[$n$,$ m$]$