

GridlandTime Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 7728 Accepted Submission(s): 3545 Problem Description For years, computer scientists have been trying to find efficient solutions to different computing problems. For some of them efficient algorithms are already available, these are the ¡°easy¡± problems like sorting, evaluating a polynomial or finding the shortest path in a graph. For the ¡°hard¡± ones only exponentialtime algorithms are known. The travelingsalesman problem belongs to this latter group. Given a set of N towns and roads between these towns, the problem is to compute the shortest path allowing a salesman to visit each of the towns once and only once and return to the starting point. The president of Gridland has hired you to design a program that calculates the length of the shortest travelingsalesman tour for the towns in the country. In Gridland, there is one town at each of the points of a rectangular grid. Roads run from every town in the directions North, Northwest, West, Southwest, South, Southeast, East, and Northeast, provided that there is a neighbouring town in that direction. The distance between neighbouring towns in directions North¨CSouth or East¨CWest is 1 unit. The length of the roads is measured by the Euclidean distance. For example, Figure 7 shows 2 ¡Á 3Gridland, i.e., a rectangular grid of dimensions 2 by 3. In 2 ¡Á 3Gridland, the shortest tour has length 6. Input The first line contains the number of scenarios. For each scenario, the grid dimensions m and n will be given as two integer numbers in a single line, separated by a single blank, satisfying 1 < m < 50 and 1 < n < 50. Output The output for each scenario begins with a line containing ¡°Scenario #i:¡±, where i is the number of the scenario starting at 1. In the next line, print the length of the shortest travelingsalesman tour rounded to two decimal digits. The output for every scenario ends with a blank line. Sample Input
Sample Output
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