Number Partitioning. You and a friend have been trekking through various far$-$off partsof the world and have accumulated a big pile of souvenirs. At the time you werent really thinking about$1$Challenge Problems $62$which of these you were planning to keep and which your friend was going to keep, but now the time hascome to divide everything up$.$Heres a way you could go about doing this. Suppose there are n objects labeled $1,2,,$ n$,$ and object ihas an agreed$-$upon value xi$.($We could think of this, for example, as a monetary resale value; the case inwhich you and your friend dont agree on the value is something we wont pursue here.$)$ One reasonable wayto divide things would be to look for a partition of the objects into two sets, so that the total value of theobjects in each set is the same.This suggests solving the following Number Partitioning Problem.You are given positive integers x$1,$ x$2,,$ xn;you want to decide whether the numbers can be partitioned into two sets S$1$ and S$2$ with the same sum:XxiS$1$xi $=$XxjS$2$xjShow that Number Partitioning is NP$-$complete.