A well-known riddle goes like this: Four people are crossing an old bridge. The bridge cannot hold more than two people at once. It is dark, so they can't walk without a flashlight, and they only have one flashlight! Furthermore, the time needed to cross the bridge varies among the people in the group. For instance, let's say that the people take 1, 2, 5 and 10 minutes to cross the bridge. When people walk together, they always walk at the speed of the slowest person. It is impossible to toss the flashlight across the bridge, so one person always has to go back with the flashlight to the others. What is the minimum amount of time needed to get all the people across the bridge?
In this instance, the answer is 17. Person number 1 and 2 cross the bridge together, spending 2 minutes. Then person 1 goes back with the flashlight, spending an additional one minute. Then person 3 and 4 cross the bridge together, spending 10 minutes. Person 2 goes back with the flashlight (2 min), and person 1 and 2 cross the bridge together (2 min). This yields a total of 2+1+10+2+2 = 17 minutes spent.
You want to create a computer program to help you solve new instances of this problem. Given an int times, where the elements represent the time each person spends on a crossing, your program should return the minimum possible amount of time spent crossing the bridge.