12 months to sing and dance in a ring their celestial dance. One after another they hold a throne. The first is young and fierce January and the last is elderly and wise December. Leaving the throne, every month cry out a digit. During a year a 12-digit number is formed. The Old Year uses this number as a shield on his way to the Abyss of Time. He defend himself with this shield from the dreadful creatures of Eternity. Because of hard blows the shield breaks to pieces corresponding to the divisors of the number.
Your task is to help the months to forge the shield for the Old Year such that it couldn’t be broken to pieces.
The first line contains a number of months that already left the throne. The second line contains the digits already cried out.
Output an arbitrary 12-digits integer that starts with the given digits and that has no nontrivial divisors. It’s guaranteed that the solution exists.
Problem Author: Pavel Atnashev
Problem Source: USU Championship 2004