4th Balkan Olympiad in Informatics
Nicosia, Cyprus, 19-25 October 1997

Day 1 - Problem 2 (1-2-3-4 MAZE)

We have a rectangle maze with dimensions nxm (where n<=20, m<=20). The top left and the bottom right positions of the maze are marked by 0, and all other maze positions by one of the numbers 1, 2, 3, 4. The aim of the game is to enter the maze at the top left corner and leave it from the bottom right corner by following the shortest path moving only to the right, left, down and up. The constraint that we have to obey in order to follow a path from the entrance to the exit is to move from a 1, to a 2, to a 3, to a 4, to a 1 and so on, in a cyclic way. From the start position you can only move to a 1 position. You can move to the exit position either from the neighboring upper or neighboring left cell of the exit position.

The first line contains the integers n and m. Each of the next n lines contains m integers representing the maze.

This file will consist of two lines, containing the number of steps and a string of characters respectively. The string consists of the characters D (for down), U (for up), L (for left) and R (for right), the steps along the shortest path to the exit.

5 4
0 1 2 3
3 2 1 4
4 1 2 1
1 4 3 2
2 3 4 0

Remark: you may assume that there is always a solution to the problem.

Time-limit for each test: 5 seconds.
Maximal score: 30 points