Max is an expert in combinatorial optimization and bitwise operations. He recently read a paper about so-called b-matchings, but it appeared to be too complicated and unnatural for him, so he decided to create his own kind of matchings and to call it -matching. He came up with a following problem.

Recall that the bitwise AND of two non-negative integers x and y is such a number x & y that it has ones in a binary representation in exactly those positions, in which both x and y also have ones in a binary representation. Define a function to be equal to a largest power of two not exceeding z if z is positive and to zero if z = 0.

You are given a complete bipartite graph (i.e. such bipartite graph that any two vertices from different parts are connected with an edge). Vertices of the first part of the graph are numbered from 1 to n₁, vertices of the second part of the graph are numbered from 1 to n₂. The i-th vertex of the first part of the graph is assigned a non-negative integer x_i, the j-th vertex of the second part of the graph is assigned a non-negative integer y_j.

Recall that the matching in a graph is such a set M of edges that no two distinct edges share a common endpoint. Define a weight of an edge connecting vertices u and v (from the first part and the second part of a graph respectively) to be (that is why it is valid to call such an object -matching in the future!)

Your task is to find a matching of a maximum possible total weight of edges.