243. Christmas Cryptarithm. The Christmas greeting $A M E R R Y X M A S T O A L L^{*}$ is a cryptarithm where each letter represents a specific decimal digit, and each word replaces a square number. Decode this message, given that, in addition, the sum of the digits in each word also matches some square.

Translate the above text into English, please retain the line breaks and format of the source text, and output the translation result directly.
243. Using the table of squares, it can be quickly determined that $A L L$ matches one of the numbers $100,144,400$ or 900, and $T O$ with 36 or 81.

The only four-digit square number whose sum of digits is a square and which has 1, 4, or 9 in the tens place is $7396=X M A S$; therefore, $A L L=$ 900. Since each letter represents only one digit, $T O$ must match 81. Then $M E R R Y$ must equal either 35224 or 34225. But of these two numbers, only the latter is a square. Thus, the decoded phrase will be

$$
\begin{array}{lllll}
9 & 34225 & 7396 & 81 & 900 .
\end{array}
$$

If we do not require the sums of the digits to match some squares, there will be a second solution to this problem:

$$
\begin{array}{lllll}
4 & 27556 & 3249 & 81 & 400 .
\end{array}
$$