Problem D
Game Rank
Each rank has a certain number of “stars” that one needs to gain before advancing to the next rank. If a player wins a game, she gains a star. If before the game the player was on rank $6$$25$, and this was the third or more consecutive win, she gains an additional bonus star for that win. When she has all the stars for her rank (see list below) and gains another star, she will instead gain one rank and have one star on the new rank.
For instance, if before a winning game the player had all the stars on her current rank, she will after the game have gained one rank and have $1$ or $2$ stars (depending on whether she got a bonus star) on the new rank. If on the other hand she had all stars except one on a rank, and won a game that also gave her a bonus star, she would gain one rank and have $1$ star on the new rank.
If a player on rank $1$$20$ loses a game, she loses a star. If a player has zero stars on a rank and loses a star, she will lose a rank and have all stars minus one on the rank below. However, one can never drop below rank $20$ (losing a game at rank $20$ with no stars will have no effect).
If a player reaches the Legend rank, she will stay legend no matter how many losses she incurs afterwards.
The number of stars on each rank are as follows:

Rank $25$$21$: $2$ stars

Rank $20$$16$: $3$ stars

Rank $15$$11$: $4$ stars

Rank $10$$1$: $5$ stars
A player starts at rank $25$ with no stars. Given the match history of a player, what is her rank at the end of the sequence of matches?
Input
The input consists of a single line describing the sequence of matches. Each character corresponds to one game; ‘W’ represents a win and ‘L’ a loss. The length of the line is between $1$ and $10\, 000$ characters (inclusive).
Output
Output a single line containing a rank after having played the given sequence of games; either an integer between $1$ and $25$ or “Legend”.
Sample Input 1  Sample Output 1 

WW 
25 
Sample Input 2  Sample Output 2 

WWW 
24 
Sample Input 3  Sample Output 3 

WWWW 
23 
Sample Input 4  Sample Output 4 

WLWLWLWL 
24 
Sample Input 5  Sample Output 5 

WWWWWWWWWLLWW 
19 
Sample Input 6  Sample Output 6 

WWWWWWWWWLWWL 
18 