kleinberg, jon. algorithm design (p.444, q.45). consider the following definition. we are given a set of n countries that are engaged in trade with one another. for each country i, we have the value si of its budget surplus; this number may be positive or negative, with a negative number indicating a deficit. for each pair of countries i, j, we have the total value eij of all exports from i to j; this number is always nonnegative. we say that a subset s of the countries is free-standing if the sum of the budget surpluses of the countries in s, minus the total value of all exports from countries in s to countries not in s, is nonnegative. give a polynomial-time algorithm that takes this data for a set of n countries and decides whether it contains a nonempty free-standing subset that is not equal to the full set.