Suppose we are given an instance of the [mathjaxinline]s-t[/mathjaxinline] shortest path problem on a directed graph [mathjaxinline]G[/mathjaxinline]. We assume that all edge cost are positive and distinct. Let [mathjaxinline]P[/mathjaxinline] be a minimum-cost [mathjaxinline]s-t[/mathjaxinline] path for this instance. Now suppose we replace each edge cost [mathjaxinline]c_e [/mathjaxinline] by its square, [mathjaxinline]c_e^2 [/mathjaxinline], thereby creating a new instance of the problem with the same graph but different costs.Decide whether you think the following statement is true or false.[mathjaxinline]P[/mathjaxinline] must still be a minimum-cost [mathjaxinline]s-t[/mathjaxinline] path for this new instance.[mathjaxinline]P[/mathjaxinline] must still be a minimum-cost [mathjaxinline]s-t[/mathjaxinline] path for this new instance.