ZOJ Problem Set - 1543
Our chemical biologists have invented a new very useful form of life called
stripies (in fact, they were first called in Russian - polosatiki, but the scientists
had to invent an English name to apply for an international patent). The stripies
are transparent amorphous amebiform creatures that live in flat colonies in
a jelly-like nutrient medium. Most of the time the stripies are moving. When
two of them collide a new stripie appears instead of them. Long observations
made by our scientists enabled them to establish that the weight of the new
stripie isn't equal to the sum of weights of two disappeared stripies that collided;
nevertheless, they soon learned that when two stripies of weights m1 and m2
collide the weight of resulting stripie equals to 2*sqrt(m1*m2). Our chemical
biologists are very anxious to know to what limits can decrease the total weight
of a given colony of stripies.
The first line of the input file contains one integer N (1 <= N <= 100) - the number of stripies in a colony. Each of next N lines contains one integer ranging from 1 to 10000 - the weight of the corresponding stripie.
Process to the end of file.
The output file must contain one line with the minimal possible total weight of colony with the accuracy of three decimal digits after the point.
Source: Northeastern Europe 2001, Northern Subregion