On an infinite plane, a robot initially stands at `(0, 0)` and faces north. Note that:

*   The **north direction** is the positive direction of the y-axis.
*   The **south direction** is the negative direction of the y-axis.
*   The **east direction** is the positive direction of the x-axis.
*   The **west direction** is the negative direction of the x-axis.

The robot can receive one of three instructions:

*   `"G "`: go straight 1 unit.
*   `"L "`: turn 90 degrees to the left (i.e., anti-clockwise direction).
*   `"R "`: turn 90 degrees to the right (i.e., clockwise direction).

The robot performs the `instructions` given in order, and repeats them forever.

Return `true` if and only if there exists a circle in the plane such that the robot never leaves the circle.

**Example 1:**

**Input:** instructions =  "GGLLGG "
**Output:** true
**Explanation:** The robot is initially at (0, 0) facing the north direction.
 "G ": move one step. Position: (0, 1). Direction: North.
 "G ": move one step. Position: (0, 2). Direction: North.
 "L ": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: West.
 "L ": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: South.
 "G ": move one step. Position: (0, 1). Direction: South.
 "G ": move one step. Position: (0, 0). Direction: South.
Repeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (0, 2) --> (0, 1) --> (0, 0).
Based on that, we return true.

**Example 2:**

**Input:** instructions =  "GG "
**Output:** false
**Explanation:** The robot is initially at (0, 0) facing the north direction.
 "G ": move one step. Position: (0, 1). Direction: North.
 "G ": move one step. Position: (0, 2). Direction: North.
Repeating the instructions, keeps advancing in the north direction and does not go into cycles.
Based on that, we return false.

**Example 3:**

**Input:** instructions =  "GL "
**Output:** true
**Explanation:** The robot is initially at (0, 0) facing the north direction.
 "G ": move one step. Position: (0, 1). Direction: North.
 "L ": turn 90 degrees anti-clockwise. Position: (0, 1). Direction: West.
 "G ": move one step. Position: (-1, 1). Direction: West.
 "L ": turn 90 degrees anti-clockwise. Position: (-1, 1). Direction: South.
 "G ": move one step. Position: (-1, 0). Direction: South.
 "L ": turn 90 degrees anti-clockwise. Position: (-1, 0). Direction: East.
 "G ": move one step. Position: (0, 0). Direction: East.
 "L ": turn 90 degrees anti-clockwise. Position: (0, 0). Direction: North.
Repeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (-1, 1) --> (-1, 0) --> (0, 0).
Based on that, we return true.

**Constraints:**

*   `1 <= instructions.length <= 100`
*   `instructions[i]` is `'G'`, `'L'` or, `'R'`.


def numRookCaptures(board):
    x, y, captures = 0, 0, 0

    for i in range(8):
        for j in range(8):
            if board[i][j] == 'R':
                x, y = i, j
                break
        if board[x][y] == 'R':
            break

    dirs = [(1, 0), (-1, 0), (0, 1), (0, -1)]
    for dx, dy in dirs:
        nx, ny = x + dx, y + dy
        while 0 <= nx < 8 and 0 <= ny < 8:
            if board[nx][ny] == 'p':
                captures += 1
                break
            elif board[nx][ny] == 'B':
                break
            nx += dx
            ny += dy

    return captures
