Problem: We have a grid with H rows and W columns. The state of the cell at the i-th (1≤i≤H) row and j-th (1≤j≤W) column is represented by a letter a_{ij}, as follows:

* `.` : This cell is empty.
* `o` : This cell contains a robot.
* `E` : This cell contains the exit. `E` occurs exactly once in the whole grid.



Snuke is trying to salvage as many robots as possible, by performing the following operation some number of times:

* Select one of the following directions: up, down, left, right. All remaining robots will move one cell in the selected direction, except when a robot would step outside the grid, in which case the robot will explode and immediately disappear from the grid. If a robot moves to the cell that contains the exit, the robot will be salvaged and immediately removed from the grid.



Find the maximum number of robots that can be salvaged.

Constraints

* 2≤H,W≤100
* a_{ij} is `.`, `o` or `E`.
* `E` occurs exactly once in the whole grid.

Input

The input is given from Standard Input in the following format:


H W
a_{11}...a_{1W}
:
a_{H1}...a_{HW}


Output

Print the maximum number of robots that can be salvaged.

Examples

Input

3 3
o.o
.Eo
ooo


Output

3


Input

2 2
E.
..


Output

0


Input

3 4
o...
o...
oooE


Output

5


Input

5 11
ooo.ooo.ooo
o.o.o...o..
ooo.oE..o..
o.o.o.o.o..
o.o.ooo.ooo


Output

12

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 er = -1, ec = -1;
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				if(map[i][j] == 'E'){
					er = i; ec = j;
				}
			}
		}
		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] == 'o' ? 1 : 0);
			}
		}
		int[][][][] dp = new int[n][][][];
		for(int i = 0;i < n;i++){
			dp[i] = new int[n-i][][];
			for(int j = 0;i+j < n;j++){
				dp[i][j] = new int[m][];
				for(int k = 0;k < m;k++){
					dp[i][j][k] = new int[m-k];
					Arrays.fill(dp[i][j][k], -99999999);
				}
			}
		}
		for(int h = 1;h <= n;h++){
			for(int w = 1;w <= m;w++){
				for(int i = 0;i+h-1 < n;i++){
					for(int j = 0;j+w-1 < m;j++){
						if(i <= er && er < i+h && j <= ec && ec < j+w){
							int k = i+h-1, l = j+w-1;
							if(h == 1 && w == 1){
								dp[i][k-i][j][l-j] = 0;
								continue;
							}
							// (r1,c1,r2,c2)
							// ((r2-er),(c2-ec), n-1-(er-r1), m-1-(ec-c1))
							if(i+1 <= k){
								dp[i][k-i][j][l-j] = Math.max(dp[i][k-i][j][l-j], dp[i+1][k-(i+1)][j][l-j]
										+ get(Math.max(i, k-er), Math.max(j, l-ec), Math.min(i, n-1-(er-(i+1))), Math.min(l, m-1-(ec-j)), cum));
							}
							if(i <= k-1){
								dp[i][k-i][j][l-j] = Math.max(dp[i][k-i][j][l-j], dp[i][k-1-i][j][l-j]
									+ get(Math.max(k, k-1-er), Math.max(j, l-ec), Math.min(k, n-1-(er-i)), Math.min(l, m-1-(ec-j)), cum));
							}
							if(j+1 <= l){
								dp[i][k-i][j][l-j] = Math.max(dp[i][k-i][j][l-j], dp[i][k-i][j+1][l-(j+1)]
										+ get(Math.max(i, k-er), Math.max(j, l-ec), Math.min(k, n-1-(er-i)), Math.min(j, m-1-(ec-(j+1))), cum));
							}
							if(j <= l-1){
								dp[i][k-i][j][l-j] = Math.max(dp[i][k-i][j][l-j], dp[i][k-i][j][l-1-j]
										+ get(Math.max(i, k-er), Math.max(l, (l-1)-ec), Math.min(k, n-1-(er-i)), Math.min(l, m-1-(ec-j)), cum));
							}
						}
					}
				}
			}
		}
		out.println(dp[0][n-1][0][m-1]);
	}
	
	static int get(int r1, int c1, int r2, int c2, int[][] cum)
	{
		if(r1 > r2 || c1 > c2)return 0;
		return cum[r2+1][c2+1] - cum[r1][c2+1] - cum[r2+1][c1] + cum[r1][c1];
	}
	
	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)); }
}