Minimax Tic-Tac-Toe

Minimax is how game-playing programs choose moves: assume both players play perfectly, score every finished game, and back the scores up the game tree. The player to move picks the child with the highest score for itself.

The board is a 9-character string read row by row (indices 0-8), with "X", "O" or "." for an empty cell. X always moves first, so it is X's turn when both have the same number of marks and O's turn otherwise.

Score a finished game from the point of view of the player to move: +1 for a win, 0 for a draw, -1 for a loss. Return the empty cell whose move has the best minimax score; if several are equally good, return the lowest index.

Implement best_move(board).

Input

board: A valid position where nobody has won yet and at least one cell is empty.

Output

Return the index (0-8) of the best move.

Constraints

board has exactly 9 characters, each X, O or .

The position is reachable in a real game, nobody has won, and at least one cell is empty

Examples

Example 1

Input:
board = "XX.OO...."

Expected output:
2

Explanation

X and O have two marks each, so X moves. Playing 2 completes the top row and wins at once (+1).

Example 2

Input:
board = "X..OO...X"

Expected output:
5

Explanation

X moves. O threatens to complete the middle row at 5. Every other move lets O win (-1), while blocking at 5 leads to a draw (0), so the answer is 5.

References

Run the sample tests to check your code without submitting.

Example 1 Not run
Input:
```
board = "XX.OO...."
```
Expected output:
```
2
```
Your output
Example 2 Not run
Input:
```
board = "X..OO...X"
```
Expected output:
```
5
```
Your output

4 hidden tests also run when you submit.

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