Mountain Walking mtwalk.X Farmer John and Bessie the cow have embarked on one of those 'active' vacations. They spend entire days walking in the mountains and then, at the end of the day, they tire and return to their vacation cabin. Since climbing requires a lot of energy and they are already tired, they wish to return to the cabin using a path that has the least difference between its highest and lowest elevations, no matter how long that path is. Help FJ find this easy-to-traverse path. The map of the mountains is given by an N x N (2 <= N <= 100) matrix of integer elevations (0 <= elevation <= 250) FJ and Bessie are currently at the upper left position (row 1, column 1) and the cabin is at the lower right (row N, column N). They can travel right, left, toward the top, or toward the bottom of the grid. They can not travel on a diagonal. PROBLEM NAME: mtwalk INPUT FORMAT: * Line 1: A single integer: N * Lines 2..N+1: Line i+1 N space-separated integers describing the elevations of row i. The first number on the line corresponds to the first (left) column of the grid, and so on. SAMPLE INPUT: 5 1 1 3 6 8 1 2 2 5 5 4 4 0 3 3 8 0 2 3 4 4 3 0 2 1 OUTPUT FORMAT: * Line 1: An integer that is the minimal height difference on the optimal path. SAMPLE OUTPUT: 2 OUTPUT DETAILS: xx... Taking the path shown here, the minimum height is 0 and the .xx.. maximum is 2, so the difference is 2. ..x.. ..x.. ..xxx