Teacher W is playing a game with his fan, Menji.

There are $n$ cards on the table, numbered $1$ to $n$. Each card has a letter $s_i$ written on it, where $s_i \in \{\texttt{X}, \texttt{W}, \texttt{M}\}$. It is guaranteed that there is at least one $\texttt{W}$ and at least one $\texttt{M}$.

Teacher W and Menji take turns, with Teacher W going first. On a player's turn, they choose an interval $[l, r]$ ($1 \leq l \leq r \leq n$) such that the interval contains no cards with the letter $\texttt{X}$, and remove all cards within that interval.

If, after any move, all $\texttt{W}$ and $\texttt{M}$ cards have been removed, the game ends in a draw. Otherwise, if after a move all $\texttt{W}$ cards have been removed, Teacher W wins. If after a move all $\texttt{M}$ cards have been removed, Menji wins.

Teacher W and Menji are both perfectly rational. Given the string $s_1 \dots s_n$, determine the outcome of the game. Output Water if Teacher W wins, Menji if Menji wins, and Draw if the game ends in a draw.

Input

The input is read from standard input.

This problem contains multiple test cases.

The first line contains an integer $T$ ($1 \leq T \leq 10^5$), representing the number of test cases.

For each test case:

A single string $s$ ($2 \leq |s| \leq 10^5$) is given, where $s_i$ is the letter on card $i$.

Output

Output to standard output.

For each test case, output a single string: Water if Teacher W wins, Menji if Menji wins, and Draw if the game ends in a draw.

Examples

Input 1

6
WMW
MWM
WMWXMWM
WWWXMMMXWWW
MMMXWWWXMMM
WMWMWMWWMWW

Output 1

Draw
Water
Draw
Menji
Water
Draw

Note 1

• For the first test case, if Teacher W removes all cards at once, the game is a draw. Otherwise, Teacher W cannot remove both $\texttt{W}$ cards at the same time, and Menji can then remove the $\texttt{M}$ card and win. Therefore, Teacher W will choose to remove all cards, resulting in a draw.

• For the second test case, Teacher W can remove the $\texttt{W}$ card directly and win.