Problem Description

Given an $n \times m$ rectangle, each cell is either _ or X. Choose the largest possible $r \times c$ rectangle such that multiple $r \times c$ rectangles (overlapping is allowed) can cover all X cells, and do not cover any _ cells.

Input Format

The first line contains $n, m$, as described above.

The next $n$ lines each contain a string of length $m$ describing the matrix.

Output Format

Output one line with two integers $r, c$, separated by a space.

If there are multiple choices with the maximum area, output the one with the smallest $r$.

4 5
_XXX_
XXXX_
XXXXX
_XXXX

2 3

Hint

Constraints: for $100\%$ of the testdata, $1 \le n, m \le 2.5 \times 10^3$.

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