# Problem 262: Mountain Range
The following equation represents the continuous topography of a
mountainous region, giving the elevation h at any point (x,y): A
mosquito intends to fly from A(200,200) to B(1400,1400), without leaving
the area given by 0 ≤ x, y ≤ 1600. Because of the intervening mountains,
it first rises straight up to a point A', having elevation f. Then,
while remaining at the same elevation f, it flies around any obstacles
until it arrives at a point B' directly above B. First, determine fmin
which is the minimum constant elevation allowing such a trip from A to
B, while remaining in the specified area. Then, find the length of the
shortest path between A' and B', while flying at that constant elevation
fmin. Give that length as your answer, rounded to three decimal places.
Note: For convenience, the elevation function shown above is repeated
below, in a form suitable for most programming languages: h=(
5000-0.005\*(x\*x+y\*y+x\*y)+12.5\*(x+y) ) \* exp(
-abs(0.000001\*(x\*x+y\*y)-0.0015\*(x+y)+0.7) )