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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		var MF = new MaxFlow_Dinic();
		int HW = H * W;
		int N = 2 * HW + 2;
		int source = 2 * HW;
		int sink = source + 1;
		MF.Init(N);
		
		int Inf = (int) 1e9;
		int rcs = 0, rct = 0;
		
		for(int i=0;i<H;i++){
			for(int j=0;j<W;j++){
				if(S[i][j] == '.') continue;
				
				if(S[i][j] == 'o') {MF.AddEdge(i * W + j, i * W + j + HW, 1);}
				if(S[i][j] == 'S') {MF.AddEdge(i * W + j, i * W + j + HW, Inf); rcs = i * W + j;}
				if(S[i][j] == 'T') {MF.AddEdge(i * W + j, i * W + j + HW, Inf); rct = i * W + j;}
				
				for(int ii=0;ii<H;ii++){
					if(ii == i) continue;
					if(S[ii][j] != '.') MF.AddEdge(i * W + j + HW, ii * W + j, Inf);
				}
				for(int jj=0;jj<W;jj++){
					if(jj == j) continue;
					if(S[i][jj] != '.') MF.AddEdge(i * W + j + HW, i * W + jj, Inf);
				}
			}
		}
		
		if(rcs / W == rct  / W || rcs % W == rct  % W){
			Console.WriteLine(-1);
			return;
		} 
		
		MF.AddEdge(source, rcs, Inf);
		MF.AddEdge(rct + HW, sink, Inf);
		
		var ans = MF.MaxFlow(source, sink);
		Console.WriteLine(ans);
		
	}
	int H,W;
	String[] S;
	public Sol(){
		var d = ria();
		H = d[0]; W = d[1];
		S = new String[H];
		for(int i=0;i<H;i++) S[i] = rs();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}


class MaxFlow_Dinic{
	// arihon is god
	class Edge {
		public int To,Cap,Rev;
		public Edge(int to = 0,int cap = 0,int rev = 0){
			To = to;
			Cap = cap;
			Rev = rev;
		}
	}
	
	List<Edge>[] G;
	int[] Level;
	int[] Iter;
	
	static int Inf = (int) 1e9;
	public int N;
	public void Init(int n){
		N = n;
		G = new List<Edge>[N];
		for(int i=0;i<N;i++) G[i] = new List<Edge>();
		Level = new int[N];
		Iter = new int[N];
	}
	
	
	public void AddEdge(int from, int to, int cap){
		G[from].Add(new Edge(to,cap,G[to].Count));
		G[to].Add(new Edge(from,0,G[from].Count-1));
	}
	
	void bfs(int s){
		for(int j=0;j<G.Length;j++)Level[j] = -1;
		var Q = new Queue<int>();
		Level[s] = 0;
		Q.Enqueue(s);
		
		while(Q.Count>0){
			var v = Q.Dequeue();
			foreach(var e in G[v]){
				if(e.Cap > 0 && Level[e.To] < 0){
					Level[e.To] = Level[v] + 1;
					Q.Enqueue(e.To);
				}
			}
		}
	}
	
	int dfs(int v, int t, int f){
		if(v == t) return f;
		for(;Iter[v] < G[v].Count; Iter[v]++){
			var e = G[v][Iter[v]];
			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[e.To][e.Rev].Cap += d;
					return d;
				}
			}
		}
		return 0;
	}
	
	public int MaxFlow(int s,int t){
		int flow = 0;
		while(true){
			bfs(s);
			if(Level[t] < 0) return flow;
			Iter = new int[N];
			
			int f;
			while( ( f = dfs(s,t,Inf)) > 0){
				flow += f;
			}
		}
	}
	
}