For{1,2,3,…,n} and each of its nonempty subsets a unique alternating sum is defined as follows: Arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers.(For examples, the alternating sum for {1,2,4,6,9} is 9-6+4-2+1=6 and for {5} it is simply 5.) Find the sum of all such alternating sums for n=7.

(第一届AIME1983 第十三题)