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.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		int h=s[0],w=s[1];
		int n=h+w;
		var t=new string[h];
		for(int i = 0;i<h;i++) {
			t[i]=sc.S;
			for(int j = 0;j<w;j++) {
				if(t[i][j]!='.'){n+=2;}
			}
		}
		var fl=new Flow(n+1);
		int inf=100000000,st=0,go=0;
		n=h+w;
		for(int i = 0;i<h;i++) {
			for(int j = 0;j<w;j++) {
				if(t[i][j]!='.'){
					fl.Edge(n,n+1,1);
					fl.Edge(i,n,inf);
					fl.Edge(n+1,i,inf);
					fl.Edge(h+j,n,inf);
					fl.Edge(n+1,h+j,inf);
					if(t[i][j]=='S'){st=n+1;}
					else if(t[i][j]=='T'){go=n;}
					n+=2;
				}
			}
		}
		int ans=fl.Dinic(st,go);
		Console.WriteLine("{0}",ans<inf?ans:-1);
	}
}
public class Flow{
	private List<int>[] li;
	private Dictionary<int,int>[] h;
	private bool[] b;
	private int[] l;
	private int n,ans,go;
	private const int inf=int.MaxValue;
	public Flow(int n){
		this.n=n;
		li=new List<int>[n];
		h=new Dictionary<int,int>[n+1];
		for(int i=0;i<n;i++){
			li[i]=new List<int>();
			h[i]=new Dictionary<int,int>();
		}
	}
	public void Edge(int a,int b,int c){
		//if(!h[a].ContainsKey(b)){
			li[a].Add(b);
			li[b].Add(a);
			h[a].Add(b,c);
			h[b].Add(a,0);
		//}
		//else{h[a][b]=c;}
	}
	public int Dinic(int st,int go){
		this.go=st;
		ans=0;
		int z=1;
		while(z>0){
			l=new int[n];
			var qu=new Queue<Tuple<int,int>>();
			qu.Enqueue(Tuple.Create(st,1));
			l[st]=1;
			while(qu.Count>0){
				var e=qu.Dequeue();
				for(int i=0;i<li[e.Item1].Count;i++){
					if(l[li[e.Item1][i]]==0&&h[e.Item1][li[e.Item1][i]]!=0){
						l[li[e.Item1][i]]=e.Item2+1;
						qu.Enqueue(Tuple.Create(li[e.Item1][i],e.Item2+1));
					}
				}
				if(e.Item1==go){break;}
			}
			b=new bool[n];
			z=Fu3(go,inf);
			ans+=z;
		}
		return ans;
	}
	private int Fu3(int a,int p){
		if(a==go){return p;}
		int u=0;
		for(int i=0;i<li[a].Count&&p>u;i++){
			if(!b[li[a][i]]&&l[li[a][i]]<l[a]&&h[li[a][i]][a]!=0){
				int z=Fu3(li[a][i],Min(p-u,h[li[a][i]][a]));
				h[li[a][i]][a]-=z;
				h[a][li[a][i]]+=z;
				u+=z;
			}
		}
		if(u==0){b[a]=true;}
		return u;
	}
	public int Ff(int st,int go){
		this.go=go;
		ans=0;
		int z=1;
		while(z>0){
			b=new bool[n];
			z=Fu2(st,inf);
			ans+=z;
		}
		return ans;
	}
	private int Fu2(int a,int p){
		if(a==go){return p;}
		int u=0;
		b[a]=true;
		for(int i=0;i<li[a].Count&&p>u;i++){
			if(!b[li[a][i]]&&h[a][li[a][i]]!=0){
				int z=Fu2(li[a][i],Min(p-u,h[a][li[a][i]]));
				h[a][li[a][i]]-=z;
				h[li[a][i]][a]+=z;
				u+=z;
			}
		}
		if(u!=0){b[a]=false;}
		return u;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}