Skiing Bessie and the rest of Farmer Ran's cows are taking a trip this winter to go skiing. One day Bessie finds herself at the top left corner of an R (1 <= R <= 100) by C (1 <= C <= 100) grid of elevations E (-25 <= E <= 25). In order to join FR and the other cows at a discow party, she must get down to the bottom right corner as quickly as she can by traveling only north, south, east, and west. Bessie starts out traveling at a initial speed V (1 <= V <= 1,000,000). She has discovered a remarkable relationship between her speed and her elevation change. When Bessie moves from a location of height A to an adjacent location of height B, her speed is multiplied by the number 2^(A-B). The time it takes Bessie to travel from a location to an adjacent location is the reciprocal of her speed when she is at the first location. Find the smallest amount of time it will take Bessie to join her cow friends. PROBLEM NAME: cowski.X INPUT FORMAT: * Line 1: Three space-separated integers: V, R, and C, which respectively represent Bessie's initial velocity and the number of rows and columns in the grid. * Lines 2..R+1: C integers representing the elevation E of the corresponding location on the grid. SAMPLE INPUT: 1 3 3 1 5 3 6 3 5 2 4 3 OUTPUT FORMAT: A single number value: the minimum amount of time that Bessie can take to reach the bottom right corner of the grid. Your output needs to be within either 1e-2 absolute error or 1e-10 relative error. SAMPLE OUTPUT: 29.00 OUTPUT DETAILS: Bessie's best route is: Start at 1,1 time 0 speed 1 East to 1,2 time 1 speed 1/16 South to 2,2 time 17 speed 1/4 South to 3,2 time 21 speed 1/8 East to 3,3 time 29 speed 1/4