Coin Turning Game

Alice and Bob play a coin game. Alice moves first.

$N$ coins lie in a row, each showing heads or tails. On a turn a player picks a block of consecutive coins and flips every coin in that block. The rightmost coin of the block must show heads before the flip, so it goes from heads to tails. A player who cannot pick such a block loses.

The initial arrangement of the coins is given. Decide whether Alice wins when both players play optimally.

The first line contains an integer $T$ ($1 \le T \le 100$), the number of test cases.

Each of the next $T$ lines contains a string $S$ ($3 \le |S| \le 15$). Every character of $S$ is H or T, where H means the coin shows heads and T means it shows tails.

Print one line for each test case.

If Alice wins, print YES p k. Here $p$ is the position of the rightmost coin she flips on her first move, counting from 1, and $k$ is the number of coins that move flips. When several first moves win, choose the one with the smallest $p$, and among those the one with the smallest $k$.

If Alice cannot win, print NO.