Problem: 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.

Examples

Input

3 3
...
.##
.##


Output

2


Input

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


Output

4

Solution (in JAVA):

Solution:
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni(), m = ni();
		char[][] map = nm(n,m);
		
		int[][] cum = new int[n+1][m+1];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				cum[i+1][j+1] = cum[i+1][j] + cum[i][j+1] - cum[i][j] + 
						(map[i][j] == '#' ? 1 : 0);
			}
		}
		
		int[][][] reach = new int[n][m][n+1];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				int l = m-1;
				for(int k = 1;i+k <= n;k++){
					for(;l >= j;l--){
						// (i,j) -> (i+k-1, l)
						long S = 
						cum[i+k][l+1] - cum[i+k][j] - cum[i][l+1] +
						cum[i][j];
						if(S == 0 || S == k*(l-j+1)){
							reach[i][j][k] = l-j+1;
							break;
						}
					}
				}
			}
		}
		
		int dep = 0;
		while(true){
			if(reach[0][0][n] == m){
				out.println(dep);
				return;
			}
			
			int[][][] tnreach = trans(nreach(trans(reach)));
			int[][][] nreach = nreach(reach);
			for(int i = 0;i < n;i++){
				for(int j = 0;j < m;j++){
					for(int k = 1;k <= n;k++){
						nreach[i][j][k] = Math.max(nreach[i][j][k], 
								tnreach[i][j][k]);
					}
				}
			}
			reach = nreach;
			dep++;
		}
	}
	
	static int[][][] nreach(int[][][] reach)
	{
		int n = reach.length, m = reach[0].length;
		int[][][] nreach = new int[n][m][n+1];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				for(int k = 1;i+k <= n;k++){
					int ne = j+reach[i][j][k];
					if(ne < m){
						nreach[i][j][k] = reach[i][ne][k] + reach[i][j][k];
					}else{
						nreach[i][j][k] = reach[i][j][k];
					}
				}
			}
		}
		return nreach;
	}
	
	static int[][][] trans(int[][][] a)
	{
		int n = a.length, m = a[0].length;
		int[][][] ret = new int[m][n][m+1];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				int z = 1;
				for(int k = n;k >= 1;k--){
					for(;z <= a[i][j][k];z++){
						ret[j][i][z] = k;
					}
				}
			}
		}
		return ret;
	}
	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}