Chess Wins and Losses

In the game of chess, players can win, lose, or draw. For the sake of this problem, we say a player is in a slump if they either:

• have more losses than combined wins and draws in the last three games
• have not had a win in the last four games

Given an input of a sequence of wins, losses and draws (depicted using characters W, L, and D), use a divide-and-conquer algorithm to determine whether the player is in a slump at any point, returning T if the player is in a slump at some point, and F otherwise.

Input format:
line 1: [single line of W, D, L characters separated by spaces, followed by a newline]

Output format:
[either T or F]

Examples

Input:
W L L L
Output:
T

From the second game, there are no wins or draws, therefore the player is in a slump after the third game.

Input:
W D L D
Output:
F

At every point, there are more wins + draws than losses. The player is therefore never in a slump

Input:
D L D D L
Output:
T

Although criteria (1) from above holds, there are no wins in 5 games, therefore the player satisfies criteria (2) and is in a slump

Input: W W L W L Output: T

After the final game, the last three games have more losses than wins, and thus form a slump.