Write a program that, given a list of the edges in a connected graph G on the vertices 1,..., n, in polynomial time outputs a Boolean formula F that is satisfiable if and only if G has a Hamiltonian path. You can assume the list of edges looks something like (1, 2) (1, 3) (4, 2) (6, 5) (5, 3) with one pair per line, and your output should consist of a single line containing copies of space, (, ), AND, OR, NOT and variables that look something like x1, x2, etc.