Suppose you have n input wires and n output wires, each directed from a source to aterminus. Each input wire meets each output wire in exactly one distinct point, at aspecial piece of hardware called a junction box. Points on the wire are naturally orderedin the direction from source to terminus; for two distinct points x and y on the samewire, we say that x is upstream from y if x is closer to the source than y, and otherwisewe say x is downstream from y. The order in which one input wire meets the outputwires in not necessarily the same as the order in which another input wire meets theoutput wires. (And similarly for the orders in which output wires meet input wires.)Each input wire is carrying a distinct data stream, and this data stream must beswitched onto one of the output wires. If the stream of Input i is switched ontoOutput j at junction box B, then this stream passes through all the junction boxesupstream of B on Input i and all the junction boxes downstream from B on Output j. It does not matter which input data stream gets switched onto which output wire, buteach input data stream must be switched onto a different output wire. Furthermore, no two data streams can pass through the same junction box following the switchingoperation. Show that for any specified pattern in which the input wires and output wires meet eachother (each pair meeting exactly once), a valid switching of the data streams can alwaysbe found – one in which each input data stream is switched onto a different output, and no two of the resulting streams pass through the same junction box. Additionally, give an algorithm to find such a valid switching and prove its correctness