Let a set  $\{1,2,3,\mathrm{....},n\}$  and for each of its non-empty subsets an alternating sum is obtained by arranging the numbers of the subset in the descending order and alternatively add and subtract successive numbers for example alternating sum of  $\{1,5,6,9,11\}$  is  $11-9+6-5+1=4.$ Then the sum of all alternating sum for