B'Define the binary encoding of a finite set of natural numbers T subseteq {0,1,2, ldots } as f(T) = sum limits_{i in T} 2^i . For example, f( {0,2 }) = 2^0 + 2^2 = 5 and f( { }) = 0 . Notice that f is a bijection from all such sets to all non-negative integers. As such, f^{-1} is also defined. You are given an integer n along with 2^n-1 sets V_1,V_2, ldots,V_{2^n-1} . Find all sets S that satisfy the following constraint: Due to the large input and output, both input and output will be given in terms of binary encodings of the sets. The first line of input contains a single integer n ( 1 <= q n <= q 20 ). The second line of input contains 2^n-1 integers v_1,v_2, ldots,v_{2^n-1} ( 0 <= q v_i < 2^{n+1} ) -- the sets V_i given in their binary encoding where V_i = f^{-1}(v_i) . The first line of output should contain an integer k indicating the number of possible S . In the following k lines, you should output f(S) for all possible S in increasing order. In the first test case, one possible S is f^{-1}(3) = {0,1 } . All the non-empty subsets T subseteq {0,1,2 } and the corresponding |S cap T| , f(T) and V_f(T) are as follows: '...