We say that a binary string s contains another binary string t if there exist indices i_{1}, i_{2}, \ldots, i_{|t|} with i_{1}< i_{2}<\ldots<i_{|t|} such that
s_{i_{1}} s_{i_{2}} \ldots s_{i_{|t|}}=t
(Tn other words, t is found as a not necessarily contiguous substring of s.) For example, 110010 contains 111. What is the length of the shortest string s which contains the binary representations of all the positive integers less than or equal to 2048?