Problem: Ksenia has a chessboard of size n × m. Each cell of the chessboard contains one of the characters: "<", ">", "^", "v", "#". The cells that contain character "#" are blocked. We know that all chessboard cells that touch the border are blocked.

Ksenia is playing with two pawns on this chessboard. Initially, she puts the pawns on the chessboard. One cell of the chessboard can contain two pawns if and only if the cell is blocked. In other cases two pawns can not stand in one cell. The game begins when Ksenia put pawns on the board. In one move, Ksenia moves each pawn to a side adjacent cell in the direction of arrows painted on the cell on which the corresponding pawn sits (if the pawn sits on "#", it does not move). Assume that Ksenia moves pawns simultaneously (see the second test case). 

Of course, Ksenia plays for points. How can one calculate the points per game? Very simply! Let's count how many movements the first pawn made and how many movements the second pawn made, sum these two numbers — it will be the resulting score of the game. 

Ksenia wonders: what is the maximum number of points she can earn (for that, she should place the pawns optimally well early in the game). Help her and find that number. 

Input

The first line contains two integers, n and m (1 ≤ n, m ≤ 2000) — the sizes of the board. Each of the following n lines contains m characters – the board's description. Each character is one of the characters: "<", ">", "^", "v", "#".

It is guaranteed that the border cells of the table are blocked cells (with character "#").

Output

If Ksenia can get infinitely many points, print -1. Otherwise, print the maximum number of points she can get.

Examples

Input

1 1
#


Output

0


Input

3 4
####
#&gt;^{}#
####


Output

3

Input

3 4
####
#&gt;&lt;#
####


Output

-1

Input

7 5
#####
##v##
##v##
#####
##^{}##
##^{}##
#####


Output

4

Input

7 5
#####
##v##
##v##
##&lt;##
##^{}##
##^{}##
#####

Output

5

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Solver {

	public static void main(String[] Args) throws NumberFormatException,
			IOException {
		new Solver().Run();
	}

	PrintWriter pw;
	StringTokenizer Stok;
	BufferedReader br;

	public String nextToken() throws IOException {
		while (Stok == null || !Stok.hasMoreTokens()) {
			Stok = new StringTokenizer(br.readLine());
		}
		return Stok.nextToken();
	}

	public int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(nextToken());
	}

	public double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}

	public long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(nextToken());
	}

	int hei, wid;
	char[][] map;
	boolean[][] isVisited;
	int[][] len;
	int maxVal=0;
	boolean isInfinity;
	boolean result;
	
	boolean findlen(int i, int j){
		if (len[i][j]>0 || map[i][j]=='#')
			return true;
		
		List<Integer> i1=new ArrayList<Integer>(), j1=new ArrayList<Integer>();
		while (len[i][j]==0 && map[i][j]!='#'){
			if (isVisited[i][j])
				return false;
			isVisited[i][j]=true;
			i1.add(i);
			j1.add(j);
			
			int i2=i;
			int j2=j;
			if (map[i][j]=='>')
				j2++;
			if (map[i][j]=='<')
				j2--;
			if (map[i][j]=='^')
				i2--;
			if (map[i][j]=='v')
				i2++;
			i=i2;
			j=j2;
			
		}
		i1.add(i);
		j1.add(j);
		for (int k=i1.size()-2; k>=0; k--){
			len[i1.get(k)][j1.get(k)]=1+len[i1.get(k+1)][j1.get(k+1)];
		}
		maxVal=Math.max(maxVal, len[i1.get(0)][j1.get(0)]);
		return true;
	}
	
	void erasePath(int i, int j){
		while (map[i][j]!='#'){
			int i2=i;
			int j2=j;
			if (map[i][j]=='>')
				j2++;
			if (map[i][j]=='<')
				j2--;
			if (map[i][j]=='^')
				i2--;
			if (map[i][j]=='v')
				i2++;
			map[i][j]='#';
			i=i2;
			j=j2;
		}
	}
	
	boolean isPath(int i, int j){
		while (len[i][j]>0){
			if (map[i][j]=='#')
				return false;
			int i2=i;
			int j2=j;
			if (map[i][j]=='>')
				j2++;
			if (map[i][j]=='<')
				j2--;
			if (map[i][j]=='^')
				i2--;
			if (map[i][j]=='v')
				i2++;
			i=i2;
			j=j2;
		}
		return true;
	}
	
	int solve(){
		len=new int[hei][wid];
		for (int i=0; i<hei; i++){
			for (int j=0; j<wid; j++){
				if (!findlen(i,j))
					return -1;
			}
		}
		if (maxVal==0)
			return 0;
		int result=maxVal*2-1;
		int i=0;
		int j=0;
		boolean found=false;
		for (i=0; i<hei && !found; i++){
			for (j=0; j<wid && !found; j++){
				if (len[i][j]==maxVal)
					found=true;
			}
		}
		i--;
		j--;
		erasePath(i,j);
		for (; i<hei; i++){
			for (j=0; j<wid; j++){
				if (len[i][j]==maxVal)
					if (isPath(i,j))
						return result+1;
			}
		}
		return result;
	}
	
	public void Run() throws NumberFormatException, IOException {
		//br = new BufferedReader(new FileReader("input.txt")); pw = new PrintWriter("output.txt");
		br=new BufferedReader(new InputStreamReader(System.in));  pw=new PrintWriter(new OutputStreamWriter(System.out));

		hei=nextInt();
		wid=nextInt();
		map=new char[hei][wid];
		for (int i=0; i<hei; i++){
			String str=br.readLine();
			for (int j=0; j<wid; j++){
				map[i][j]=str.charAt(j);
			}
		}
		
		isVisited=new boolean[hei][wid];
		int result=solve();
		pw.println(result);
		pw.flush();
		pw.close();
	}

}