Parenthesize an Arithmetic Expression Suppose you are given a sequence of n nonnegative numbers separated by n$-1$ addition $(+)$ and and multiplication $($x$)$ operators, e$.$g$.,2$x$3$ x $0+6+2$ x $5+4.$ Depending on how you parenthesize the expression it may evaluate to different values, e$.$g$.,$ for the expression above:

$((2$ x $3)$ x $(0+6))+(2$ x $(5+4))=54$

$(2$ x $3)(0+(6+2)(5+4)))=432$

$(2$ x $(3$ x $0))+(6+((2$ x $5)+4))=20$

Given a list of n integers seperated by $+$ and $*$ signs we want to compute the smallest possible value we can obtain by inserting paraenthesses your input is an array A$[1.....\mathrm{.}2$n$-1]$ where each A$[$i$]$ is an integer if i is odd and $+$ and $*$ if i is even

G$$ven A$.$ write down recursive formulation of the minumun possible value of the expressions