You are given a set Y of ndistinct positive integers y₁, y₂, ..., y_n.

Set X of ndistinct positive integers x₁, x₂, ..., x_n is said to generate set Y if one can transform X to Y by applying some number of the following two operation to integers in X:

1. Take any integer x_i and multiply it by two, i.e. replace x_i with 2·x_i.
2. Take any integer x_i, multiply it by two and add one, i.e. replace x_i with 2·x_i + 1.

Note that integers in X are not required to be distinct after each operation.

Two sets of distinct integers X and Y are equal if they are equal as sets. In other words, if we write elements of the sets in the array in the increasing order, these arrays would be equal.

Note, that any set of integers (or its permutation) generates itself.

You are given a set Y and have to find a set X that generates Y and the maximum element of X is mininum possible.