Background

The days are short and the nights are long as the winter solstice approaches. The river is cold and pitch-black, yet pink clouds rise in the east. Outside the window, sleepy seagulls and egrets form lines; inside the room, fragrance fills the air as morning cooking begins.

Study by day and work by dusk make one drowsy. In the quiet of night, one reads until the lamp burns out and then sleeps. Please help share the heavy work, so we can dance freely and have a smooth birthday.

Problem Description

There is an unwritten rule in K's home. If there are only K and H at home, they decide who cooks by playing a game called “Three-Step Gomoku”. Its rules are somewhat similar to Gomoku. As is well known, Gomoku is a game where the first player to connect five of their own pieces wins. Similarly, in Three-Step Gomoku, the two players take turns placing pieces on a grid board, and the winner is determined by whether a specified pattern is formed. Different from Gomoku:

1. Three-Step Gomoku does not distinguish between the two players' pieces. That is, you may assume both players use pieces of the same color.

2. When judging, the specified pattern cannot be rotated.

3. If the specified pattern is formed and the total number of pieces on the board is exactly a multiple of $3$, then the player who formed the pattern wins; otherwise, that player is judged to lose (i.e., the opponent wins).

For example, if the specified pattern is

.o
oo

and the current board is

o..o.
o.o..
oo...
o.o..
o..o.

then we consider that the given polyline-shaped pattern has not been formed, where o represents a piece and . represents an empty cell. But if a piece is placed next at row $2$, column $2$, then the given pattern is formed. The corresponding pieces are marked with @:

o..o.
o@o..
@@...
o.o..
o..o.

At this time, there are exactly $11$ pieces on the board, and $11$ is not a multiple of $3$, so the player who placed this piece, i.e. the first player, loses this round.

In K's home, to save time, they usually play Three-Step Gomoku on an initially empty $5\times 5$ board. Also, each time they randomly choose one 4-connected pattern consisting of at most $4$ pieces. Clearly, there is no draw in Three-Step Gomoku, so K and H agree that the loser is responsible for cooking. K wants to know, if both she and H are smart enough, whether the Three-Step Gomoku game with the chosen pattern is a first-player win; because if she can win more easily, she will secretly go easy on her younger sister.

Input Format

The input file contains multiple test cases.

The first line contains a positive integer $T$, denoting the number of test cases. It is guaranteed that $1\le T\le 200$.

For each test case, the input consists of $5$ lines. Each line contains a string of length $5$ consisting only of . and o, representing the specified pattern. It is guaranteed that in each test case, o appears at least once, and all o form a 4-connected block of size at most $4$.

Output Format

For each test case, output one line. If the input pattern is a first-player win, output Far; otherwise output Away.

3
.....
oo...
.....
.....
.....
.o...
.o...
.....
.....
.....
.....
.....
.....
.ooo.
.....

Far
Far
Away

Hint

Explanation of Sample #1

This sample contains three test cases.

In the first test case, the input pattern is oo in row $1$, column $2$. Obviously, no matter where the first player places their piece on the board, the second player has only two strategies:

• Connect with the first player's piece to form oo. At this time there are only $2$ pieces on the board, so the second player immediately loses.

• Do not connect with the first player's piece to form oo. But then it is the first player's turn, and the first player can form oo anywhere. At this time there are exactly $3$ pieces on the board, so the first player wins.

No matter which strategy is used, the second player cannot win. Therefore, for oo the game is a first-player win.

In the second test case, the input pattern is a $2$-row $1$-column pattern. By the same reasoning as oo, it is also a first-player win.

In the third test case, the input pattern is ooo in a $1$-row $3$-column shape. It can be proven that the first player must lose.

Subtasks

It is guaranteed that $1\le T\le 200$. For each test case, it is guaranteed that in the $5\times 5$ character matrix consisting of . and o, there is at least one o, and all o form a 4-connected block of size at most $4$.

Problem License

From the THUPC2024 Preliminary (Tsinghua University Student Programming Contest and Collegiate Invitational, 2024) preliminary round.

The following “this repository” refers to the THUPC2024 Preliminary official repository (https://github.com/ckw20/thupc2024_pre_public).

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Translated by ChatGPT 5