I've been trying to solve this problem on Codeforces:Challenge description:After a hard day Vitaly got very hungry and he wants to eat his  favorite potato pie. But it's not that simple. Vitaly is in the first  room of the house with n room located in a line and numbered starting  from one from left to right. You can go from the first room to the  second room, from the second room to the third room and so on  you  can go from the (n-1)-th room to the n-th room. Thus, you can go to  room x only from room x-1.The potato pie is located in the n-th room and Vitaly needs to go  there.Each pair of consecutive rooms has a door between them. In order to go  to room x from room x-1, you need to open the door between the rooms  with the corresponding key.In total the house has several types of doors (represented by  uppercase Latin letters) and several types of keys (represented by  lowercase Latin letters). The key of type t can open the door of type  T if and only if t and T are the same letter, written in different  cases. For example, key f can open door F.Each of the first n-1 rooms contains exactly one key of some type  that Vitaly can use to get to next rooms. Once the door is open with  some key, Vitaly won't get the key from the keyhole but he will  immediately run into the next room. In other words, each key can open  no more than one door.Vitaly realizes that he may end up in some room without the key that  opens the door to the next room. Before the start his run for the  potato pie Vitaly can buy any number of keys of any type that is  guaranteed to get to room n.Given the plan of the house, Vitaly wants to know what is the minimum  number of keys he needs to buy to surely get to the room n, which has  a delicious potato pie. Write a program that will help Vitaly find out  this number.InputThe first line of the input contains a positive integer n  (2n105)  the number of rooms in the house.The second line of the input contains string s of length 2n-2.  Let's number the elements of the string from left to right, starting  from one.The odd positions in the given string s contain lowercase Latin  letters  the types of the keys that lie in the corresponding rooms.  Thus, each odd position i of the given string s contains a lowercase  Latin letter  the type of the key that lies in room number  (i+1)/2.The even positions in the given string contain uppercase Latin letters   the types of doors between the rooms. Thus, each even position i of  the given string s contains an uppercase letter  the type of the door  that leads from room i/2 to room i/2+1.OutputPrint the only integer  the minimum number of keys that Vitaly needs  to buy to surely get from room one to room n.I keep exceeding time limit on one of the test cases. I made several changes (i.e. using try/except instead of 'if a in b') to my program but it still can't pass that test.My last version is this:x = input()pos = input()keys = []keys_short = []toBuy = 0for i in pos:    if i.islower():        keys.append(i)        keys_short = list(set(keys))    else:        try:            b = keys_short.index(i.lower())        except ValueError:            toBuy += 1        else:                          keys.remove(i.lower())            keys_short = list(set(keys))print(toBuy)Can you suggest any changes to make it faster?
Vitaly & Pie Programming challenge
python;performance;programming challenge;time limit exceeded
Correctness. It is possible that Vitaly on his way picks up multiple keys of the same kind. Your code implies that there is no more than one of each kind.Performance. As suggested in comments, conversions back and forth from lists to sets are expensive. A dictionary key_type: key_count is most likely what you need.