Greedy Algorithms, Inc. offers the following string-processing service. Each string submitted for processing has a starting price of 1 dollar. The customer can then ask for any two adjacent characters in the string to be swapped. This may be done an arbitrary number of times, but each swap doubles the price for processing the string. Then the company returns the modified string and charges the customer 2^{S} dollars, where S is the number of swaps executed. If a customer submits all permutations of the string PUMAC for processing and wants all of the strings to be identical after processing, what is the lowest price, in dollars, she could pay?