The Die Is Cast

According to a usually reliable (but unnamed) source, a dangerous group has decided to let chance pick the moment of their move: they roll several dice, and the instant every die shows six dots on top is their signal to act.

The police can obtain a snapshot of the dice at any moment from nearby cameras, and they want a program that reads such a bitmap image and reports the outcome of the throw — that is, the number of dots visible on each die.

The input images use only three kinds of pixels: background, die body, and die dot. Two pixels are considered connected only if they share an edge; touching at a single corner is not enough. In the figure below, pixels A and B are connected, but B and C are not.

A set $S$ of pixels is connected if, for every pair of pixels $a$, $b$ in $S$, there is a sequence $a_1, a_2, \ldots, a_k$ of pixels in $S$ with $a = a_1$, $b = a_k$, and every adjacent pair $a_i$, $a_{i+1}$ connected.

Each maximal connected set of non-background pixels (die-body and dot pixels together) is a die: "maximal" means you cannot add any other non-background pixel without breaking connectivity. Likewise, each maximal connected set of dot pixels forms a single dot.

The input contains pictures of several dice throws. Each picture starts with a line holding two integers $H$ and $W$ — the height and the width of the picture ($1 \le W, H \le 500$).

The next $H$ lines contain $W$ characters each:

• . — a background pixel,
• * — a die-body pixel,
• X — a die-dot pixel.

Every picture contains at least one die, and each die shows between $1$ and $6$ dots, inclusive. The number of dice is limited only by the picture size.

Dice and dots may have different sizes and need not be perfectly square, because of optical distortion; as long as each stays connected it may in fact have any shape. You may assume the dice are not "hollow": if every pixel outside the picture is treated as background, then all background pixels are connected.

The input ends with a picture whose first line is 0 0; that picture must not be processed.

For each throw, print a single line: the text Throw:, then a space, then the numbers of dots on the dice in that picture, sorted in increasing order and separated by single spaces.