Problem:
Score : 800 points

Problem Statement

There is a pond with a rectangular shape.
The pond is divided into a grid with H rows and W columns of squares.
We will denote the square at the i-th row from the top and j-th column from the left by (i,\ j).

Some of the squares in the pond contains a lotus leaf floating on the water.
On one of those leaves, S, there is a frog trying to get to another leaf T.
The state of square (i,\ j) is given to you by a character a_{ij}, as follows:

. : A square without a leaf.

o : A square with a leaf floating on the water.

S : A square with the leaf S.

T : A square with the leaf T.

The frog will repeatedly perform the following action to get to the leaf T: "jump to a leaf that is in the same row or the same column as the leaf where the frog is currently located."

Snuke is trying to remove some of the leaves, other than S and T, so that the frog cannot get to the leaf T.
Determine whether this objective is achievable. If it is achievable, find the minimum necessary number of leaves to remove.

Constraints

2 ≤ H, W ≤ 100

a_{ij} is ., o, S or T.

There is exactly one S among a_{ij}.

There is exactly one T among a_{ij}.

Input

Input is given from Standard Input in the following format:

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

Output

If the objective is achievable, print the minimum necessary number of leaves to remove.
Otherwise, print -1 instead.

Sample Input 1

3 3
S.o
.o.
o.T

Sample Output 1

2

Remove the upper-right and lower-left leaves.

Sample Input 2

3 4
S...
.oo.
...T

Sample Output 2

0

Sample Input 3

4 3
.S.
.o.
.o.
.T.

Sample Output 3

-1

Sample Input 4

10 10
.o...o..o.
....o.....
....oo.oo.
..oooo..o.
....oo....
..o..o....
o..o....So
o....T....
....o.....
........oo

Sample Output 4

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.PriorityQueue;

public class Main {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/D4";

	FastScanner in;
	PrintWriter out;
	
	int N, M;
	int toNode(int y, int x) {
		return y * M + x;
	}
	
	/*------------Dinic(Max Flow)------------*/
	class Dinic {
		class Edge {
			int to, cap;
			int flow = 0;
			Edge rev;
			
			Edge(int to, int cap) {
				this.to = to;
				this.cap = cap;
			}
			
			void setRevEdge(Edge rev) {
				this.rev = rev;
			}
		}
		
		int N;
		int tank;
		int[] ptr, Q, dist;
		
		ArrayList<Edge>[] g;

		public Dinic(int N) {
			this.N = N;
			g = new ArrayList[N + 2];
			for (int i = 0; i < N + 2; i++)
				g[i] = new ArrayList<Edge>();
			
			ptr = new int[N + 2];
			Q = new int[N + 2];
			dist = new int[N + 2];
		}
		
		public void addEdge(int from, int to, int cap) {
			Edge e1 = new Edge(to, cap);
			Edge e2 = new Edge(from, 0);
			e1.setRevEdge(e2);
			e2.setRevEdge(e1);
			g[from].add(e1);
			g[to].add(e2);
		}
		
		boolean dinic_bfs(int src)	{
			Arrays.fill(dist, -1);
			dist[src] = 0;
			int sizeQ = 0;
			Q[sizeQ++] = src;
			for (int i = 0; i < sizeQ; i++) {
				int u = Q[i];
				for (Edge e : g[u]) {
					if (dist[e.to] < 0 && e.flow < e.cap) {
						dist[e.to] = dist[u] + 1;
						Q[sizeQ++] = e.to;
					}
				}
			}
			return dist[tank] >= 0;
		}
		
		int dinic_dfs(int u, int f) {
			if (u == tank) return f;
			for ( ; ptr[u] < g[u].size(); ptr[u]++) {
				Edge e = g[u].get(ptr[u]);
				if (dist[e.to] == dist[u] + 1 && e.flow < e.cap) {
					int df = dinic_dfs(e.to, Math.min(f, e.cap - e.flow));
					if (df > 0) {
						e.flow += df;
						e.rev.flow -= df;
						return df;
					}
				}
			}
			
			return 0;
		}
		
		public int getMaxFlow(int src, int tank) {
			this.tank = tank;
			
			int res = 0;
			while (dinic_bfs(src)) {
				Arrays.fill(ptr, 0);
				while (true) {
					int df = dinic_dfs(src, Integer.MAX_VALUE);
					if (df == 0) break;
					res += df;
				}
			}
			
			return res;
		}

		public void addBiEdge(int from, int to, int cap) {
			Edge e1 = new Edge(to, cap);
			Edge e2 = new Edge(from, cap);
			e1.setRevEdge(e2);
			e2.setRevEdge(e1);
			g[from].add(e1);
			g[to].add(e2);
		}
	}
	/*-----------------end---------------------*/
		
	final int INF = 100000;
	public void solve() {
		N = in.nextInt();
		M = in.nextInt();
		String[] map = in.nextStringArray(N);
		
		Dinic dinic = new Dinic(N + M);
		
		int s = 0, t = N + M + 1;
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < M; j++) {
				if (map[i].charAt(j) == '.') continue; 
				
				if (map[i].charAt(j) == 'S') {
					dinic.addEdge(s, i, INF);
					dinic.addEdge(s, j + N, INF);
				} else if (map[i].charAt(j) == 'T') {
					dinic.addEdge(i, t, INF);
					dinic.addEdge(j + N, t, INF);
				} else {
					dinic.addBiEdge(i, j + N, 1);
				}
			}
		}
		long res = dinic.getMaxFlow(s, t);
		System.out.println(res == INF ? -1 : res);
	}
	
	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				// TODO 自動生成された catch ブロック
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);

		solve();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}