Problem:
Score : 1000 points

Problem Statement

Note the unusual memory limit.

For a rectangular grid where each square is painted white or black, we define its complexity as follows:

If all the squares are black or all the squares are white, the complexity is 0.

Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.

You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.

Find the complexity of the given grid.

Constraints

1 \leq H,W \leq 185

A_{ij} is # or ..

Input

Input is given from Standard Input in the following format:

H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the complexity of the given grid.

Sample Input 1

3 3
...
.##
.##

Sample Output 1

2

Let us divide the grid by the boundary line between the first and second columns.
The subgrid consisting of the first column has the complexity of 0, and the subgrid consisting of the second and third columns has the complexity of 1, so the whole grid has the complexity of at most 2.

Sample Input 2

6 7
.####.#
#....#.
#....#.
#....#.
.####.#
#....##

Sample Output 2

4

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;

class ContestReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;
  
  ContestReader(InputStream in) {
    reader = new BufferedReader(new InputStreamReader(in));
  }
  
  public String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }
  
  public int nextInt() {
    return Integer.parseInt(next());
  }
  
  public long nextLong() {
    return Long.parseLong(next());
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
}

class Solver {
  int h;
  int w;
  char[][] map;
  HashMap<Integer, Integer> dptable;
  
  private int pack(int hMin, int hMax, int wMin, int wMax) {
    return
      (hMin << 24) |
      (hMax << 16) |
      (wMin << 8) |
      wMax;
  }
  
  private int getHMin(int num) {
    return (num >> 24) & 0xFF;
  }
  
  private int getHMax(int num) {
    return (num >> 16) & 0xFF;
  }
  
  private int getWMin(int num) {
    return (num >> 8) & 0xFF;
  }
  
  private int getWMax(int num) {
    return num & 0xFF;
  }
  
  private boolean same(int hMin, int hMax, int wMin, int wMax) {
    for (int i = hMin; i < hMax; i++) {
      for (int j = wMin; j < wMax; j++) {
        if (map[hMin][wMin] != map[i][j]) {
          return false;
        }
      }
    }
    return true;
  }
  
  private int solveDfs(int hMin, int hMax, int wMin, int wMax) {
    int packIndex = pack(hMin, hMax, wMin, wMax);
    Integer cacheValue = dptable.get(packIndex);
    if (cacheValue != null) {
      return cacheValue;
    }
    if (same(hMin, hMax, wMin, wMax)) {
      dptable.put(packIndex, 0);
      return 0;
    }
    int minValue = Integer.MAX_VALUE;
    for (int hSplit = hMin + 1; hSplit < hMax; hSplit++) {
      int v1 = solveDfs(hMin, hSplit, wMin, wMax);
      int v2 = solveDfs(hSplit, hMax, wMin, wMax);
      minValue = Math.min(minValue, Math.max(v1, v2) + 1);
    }
    for (int wSplit = wMin + 1; wSplit < wMax; wSplit++) {
      int v1 = solveDfs(hMin, hMax, wMin, wSplit);
      int v2 = solveDfs(hMin, hMax, wSplit, wMax);
      minValue = Math.min(minValue, Math.max(v1, v2) + 1);
    }
    dptable.put(packIndex, minValue);
    return minValue;
  }
  
  
  public int solve(int h, int w, char[][] map) {
    this.h = h;
    this.w = w;
    this.map = map;
    this.dptable = new HashMap<>();
    
    return solveDfs(0, h, 0, w);
  }
}

public class Main {
  private static void execute(ContestReader reader, PrintWriter out) {
    int h = reader.nextInt();
    int w = reader.nextInt();
    
    char[][] map = new char[h][];
    for (int i = 0; i < h; i++) {
      map[i] = reader.next().toCharArray();
    }
    
    System.out.println(new Solver().solve(h, w, map));
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}