Addon

Scientists discovered a new radioactive element called addon. It turned out to be the most efficient nuclear fuel ever known, so it was decided to build an addon reactor. According to the design, a fuel chamber is a vertical pipe. Fuel rods, that is addon cylinders, are placed in the chamber one above another. Fuel rods can have various lengths.

A reactor cycle begins with putting fuel rods into the chamber and then igniting them. Unfortunately, the height of a column of fuel cannot be arbitrary: only certain heights keep the reaction safe. Such heights are called stable heights.

The designers have two things to decide: the height of the fuel chamber and the set of lengths in which addon rods will be produced. A set of lengths is safe (for a given chamber) if for every column built from rods whose lengths belong to this set and that is not taller than the chamber, the height of the column is stable. A set of lengths is complete (for a given chamber) if every column of a stable height that is not taller than the chamber can be built from rods whose lengths are taken from this set.

Write a program that:

• reads the set of stable heights from standard input,
• computes the maximal height of a chamber for which a safe and complete set of lengths exists,
• finds, for such a chamber, a safe and complete set of lengths with the smallest possible number of elements,
• writes the result to standard output.

The first line of standard input contains a natural number $n$ ($1 \le n \le 10\,000$), the number of given stable heights. Each of the next $n$ lines contains one positive integer no greater than $10\,000$. These numbers are the stable heights, given in increasing order.

The first line of standard output should contain one integer: the maximal height of a chamber. The following lines should contain the computed set of lengths in increasing order, one number per line.