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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;

public class Main {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		MyInput in = new MyInput(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static long LINF = 1L << 55;
	static int MOD = 1000000007;
	static int[] mh4 = { 0, -1, 1, 0 };
	static int[] mw4 = { -1, 0, 0, 1 };
	static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
	static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

	static class TaskX {

		int h, w;
		public void solve(int testNumber, MyInput in, PrintWriter out) {

			h = in.nextInt(); w = in.nextInt();
			Dinic dinic = new Dinic(h * w + 2);

			char[][] s = in.next2DChars(h, w);
			int src = h * w, dst = h * w + 1;

			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					if (s[i][j] == 'S') {
						dinic.addEdge(src, i, INF);
						dinic.addEdge(src, h + j, INF);
						s[i][j] = 'o';
					}
					if (s[i][j] == 'T') {
						dinic.addEdge(i, dst, INF);
						dinic.addEdge(h + j, dst, INF);
						s[i][j] = 'o';
					}
					if (s[i][j] == 'o') {
						dinic.addEdge(i, h + j, 1);
						dinic.addEdge(h + j, i, 1);
					}
				}
			}

			int ans = dinic.maxFlow(src, dst);
			out.println(ans == INF ? -1 : ans);

		}

		class Dinic {

			private class Edge {
				int to, cap, rev;

				public Edge(int to, int cap, int rev) {
					this.to = to;
					this.cap = cap;
					this.rev = rev;
				}
			}

			ArrayList<ArrayList<Edge>> g;
			int[] level, iter;

			public Dinic(int V) {
				g = new ArrayList<>(V);
				for (int i = 0; i < V; i++) g.add(new ArrayList<>());
				level = new int[V];
				iter = new int[V];
			}

			void addEdge(int from, int to, int capacity) {
				g.get(from).add(new Edge(to, capacity, g.get(to).size()));
				g.get(to).add(new Edge(from, 0, g.get(from).size() -1));
			}

			void bfs(int s) {
				Arrays.fill(level, -1);
				ArrayDeque<Integer> q = new ArrayDeque<>();
				level[s] = 0;
				q.add(s);

				while (!q.isEmpty()) {
					int v = q.poll();
					for (Edge e : g.get(v)) {
						if (e.cap > 0 && level[e.to] < 0) {
							level[e.to] = level[v] + 1;
							q.add(e.to);
						}
					}
				}
			}

			int dfs(int v, int t, int f) {
				if (v == t) return f;
				for (int i = iter[v]; i < g.get(v).size(); i++) {
					Edge e = g.get(v).get(i);
					if (e.cap > 0 && level[v] < level[e.to]) {
						int d = dfs(e.to, t, Math.min(f, e.cap));
						if (d > 0) {
							e.cap -= d;
							g.get(e.to).get(e.rev).cap += d;
							return d;
						}
					}
				}
				return 0;
			}

			int maxFlow(int s, int t) {
				int flow = 0;
				while (true) {
					bfs(s);
					if (level[t] < 0) return flow;
					Arrays.fill(iter, 0);
					int f;
					while ((f = dfs(s, t, Integer.MAX_VALUE)) > 0) {
						flow += f;
					}
				}
			}
		}

		int f(int i,int j) {
			return i * w + j;
		}

		boolean isInside(int i, int j) {
			return 0 <= i && i < h && 0 <= j && j < w;
		}
	}

	static class MyInput {
		private final BufferedReader in;
		private static int pos;
		private static int readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500 * 8 * 2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for (int i = 0; i < 10; i++) {
				isDigit['0' + i] = true;
			}
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public MyInput(InputStream is) {
			in = new BufferedReader(new InputStreamReader(is));
		}

		public int read() {
			if (pos >= readLen) {
				pos = 0;
				try {
					readLen = in.read(buffer);
				} catch (IOException e) {
					throw new RuntimeException();
				}
				if (readLen <= 0) {
					throw new MyInput.EndOfFileRuntimeException();
				}
			}
			return buffer[pos++];
		}

		public int nextInt() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			int ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public long nextLong() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			long ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public char nextChar() {
			while (true) {
				final int c = read();
				if (!isSpace[c]) {
					return (char) c;
				}
			}
		}

		public String nextString() {
			return new String(nextChars());
		}

		public char[] nextChars() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			return Arrays.copyOf(str, len);
		}

		public char[][] next2DChars(int h, int w) {
			char[][] s = new char[h][w];
			for (int i = 0; i < h; i++) {
				s[i] = nextChars();
			}
			return s;
		}

		int reads(int len, boolean[] accept) {
			try {
				while (true) {
					final int c = read();
					if (accept[c]) {
						break;
					}
					if (str.length == len) {
						char[] rep = new char[str.length * 3 / 2];
						System.arraycopy(str, 0, rep, 0, str.length);
						str = rep;
					}
					str[len++] = (char) c;
				}
			} catch (MyInput.EndOfFileRuntimeException e) {
			}
			return len;
		}

		public int[] nextIntArray(final int n) {
			final int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[] nextIntArray1Index(final int n) {
			final int[] res = new int[n + 1];
			for (int i = 1; i < n + 1; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[] nextIntArrayDec(final int n) {
			final int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt() - 1;
			}
			return res;
		}

		public long[] nextLongArray(final int n) {
			final long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public long[] nextLongArray1Index(final int n) {
			final long[] res = new long[n + 1];
			for (int i = 1; i < n + 1; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public long[] nextLongArrayDec(final int n) {
			final long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong() - 1;
			}
			return res;
		}

		public double nextDouble() {
			return Double.parseDouble(nextString());
		}

		public double[] nextDoubleArray(int n) {
			double[] res = new double[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

		static class EndOfFileRuntimeException extends RuntimeException {
		}

	}

}