Finding Optimal Camp Location

Problem

You are given a 2D grid of size M × N. The grid contains three kinds of cells:

• # – an obstacle (impassable)
• (whitespace) – a road (passable)
• P – a point of interest (passable)

Your task is to choose a single cell to place a camp. The camp must be reachable from every P and should minimize the sum of Manhattan distances to all P cells. Manhattan distance between two cells (r1, c1) and (r2, c2) is |r1 - r2| + |c1 - c2|.

If multiple cells achieve the same minimum total distance, pick the one with the smallest row index; if there is still a tie, pick the one with the smallest column index.

You may assume that every P is reachable from the chosen camp cell.

Input

• First line: two integers M and N – the number of rows and columns.
• Next M lines: each line is a string of length N representing a row of the grid.

Output

Print two space-separated integers: the row and column indices (0‑based) of the best camp location.

Examples

Example 1

Input:
5 5
#####
# P #
#   #
#P P#
#####

Output:
2 2

Explanation: The cell at (2,2) is the only road cell that is reachable from all three P points. Its total Manhattan distance to the Ps is minimized.

Example 2

Input:
3 4
 # P
P # 
   P

Output:
1 1

Explanation: The cell (1,1) is a road cell reachable from all three Ps. The sum of distances from (1,1) to the Ps at (0,2), (1,0), and (2,3) is |1-0|+|1-2| + |1-1|+|1-0| + |1-2|+|1-3| = 1+1 + 0+1 + 1+2 = 6, which is the smallest possible total.

Constraints

• $1 \le M, N \le 100$
• The grid contains only the characters #, (space), and P.
• There is at least one P.
• A valid camp location always exists.