You are given an array board of length N$,$ describing subsequent positions on a game board from left to right. Every position is either empty $($represented by $0$ in the array$)$ or contains a single game piece $($represented by $1).$ Each game piece can be moved at most once. A move means going one or more positions to either the left or the right. Pieces cannot capture $($occupy another piece's position$)$ or jump over each other. When the game piece is moved by X positions $($either left or right$),$ we say it travels distance X$.$ Also, pieces can be moved in any order, but they must be moved onlyone at a time.What is the maximum possible distance that the game pieces can travel altogether?Write a function:class Solution $($ public int solution$($int$[]$ board$)$; $\}$that$,$ given an array board consisting of N integers $($Os and$/$or $1$s$),$ returns the maximum total distance the game pieces can travel altogether, under the constraint that each of them is moved at most once.Examples:$1.$ Given board $[1,1,0,0,1],$ your function should return $4.$ The piece at position $0$ cannot be moved at first, but after moving the piece at position $1$ to position $3,$ the former can be moved to position $2.$ The row ends in the following configuration: $[0,0,1,1,1).$ Total traveled distance is $2+2=4.$ Thereare no combinations of moves that would produce a larger total$\mathrm{.}2.$ Given board $=[0,1],$ your function should return $1.$ The only piece can be moved one position to the left$\mathrm{.}3.$ Given board $10,0,0),$ your function should return $0.$ There are no pieces, so nothing can be moved.Write an efficient algorithm for the following assumptions:N is an integer within the range $[1.\mathrm{.}40,000$ array board contains only integers $1$ and$/$or $0$