Autocomplete

For this question, we first give you a series of n words. For every word, we first add it to our dictionary, and then we type out the word using the minimum number of strokes to autocomplete the word. What is the minimum total number of strokes needed to type out all the words?

Constraints

1 <= n <= 100001

Sum of the lengths of all the strings will not exceed 100001.

Words will only have lowercase letters.

Similar to an actual dictionary, assume that the input will not have any duplicate words.

Examples:

Example 1:

Input 1: words = ["hi", "hello", "bojack", "hills", "hill"]

Output 1: 11

Explanation:

We put "hi" in our dictionary and then we only need to type out "h", which is 1 stroke, before it autocompletes to "hi". We put "hello" in our dictionary and then we only need to type out "he", which is 2 strokes, before it autocompletes to "hello". We put "bojack" in our dictionary and then we only need to type out "b" which is 1 stroke, before it autocompletes to "bojack". We put "hills" in our dictionary and then we only need to type out "hil"(since we have "hi") which is 3 strokes, before it autocompletes to "hills". Lastly, we put "hill" in our dictionary and we need to type out "hill" which is 4 strokes. Adding these strokes up we have 1 + 2 + 1 + 3 + 4 = 11 which we then output.