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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
	#include <boost/multiprecision/cpp_int.hpp>
	#include <boost/multiprecision/cpp_dec_float.hpp>
	using bll = boost::multiprecision::cpp_int;
	using bdouble = boost::multiprecision::cpp_dec_float_100;
#endif
#ifdef LOCAL_DEV
	void debug_impl() { std::cerr << std::endl; }
	template<typename Head, typename... Tail> void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) { std::cerr << std::boolalpha << "(" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); std::cerr << std::noboolalpha; }
#else
	#define debug(...) {}
#endif
#ifdef LOCAL_TEST
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE
	#include <boost/stacktrace.hpp>
	template<typename T> class dvector : public std::vector<T> {
	public:
		dvector() : std::vector<T>() {}
		explicit dvector(size_t n, const T& value = T()) : std::vector<T>(n, value) {}
		dvector(const std::vector<T>& v) : std::vector<T>(v) {}
		dvector(const std::initializer_list<T> il) : std::vector<T>(il) {}
		dvector(const typename std::vector<T>::iterator first, const typename std::vector<T>::iterator last) : std::vector<T>(first, last) {}
		dvector(const std::string::iterator first, const std::string::iterator last) : std::vector<T>(first, last) {}
		T& operator[](size_t n) {
			try { return this->at(n); } catch (const std::exception& e) {
				std::cerr << boost::stacktrace::stacktrace() << std::endl; return this->at(n);
			}
		}
		const T& operator[](size_t n) const {
			try { return this->at(n); } catch (const std::exception& e) {
				std::cerr << boost::stacktrace::stacktrace() << std::endl; return this->at(n);
			}
		}
	};
	class dbool {
	private:
		bool boolvalue;
	public:
		dbool() : boolvalue(false) {}
		dbool(bool b) : boolvalue(b) {}
		dbool(const dbool &b) : boolvalue(b.boolvalue) {}
		operator bool&() { return boolvalue; }
		operator const bool&() const { return boolvalue; }
	};
	template<typename T> std::ostream& operator<<(std::ostream& s, const dvector<T>& v) {
		for (int i = 0, len = v.size(); i < len; ++i){ s << v[i]; if (i < len - 1) s << "\t"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const dvector< dvector<T> >& vv) {
		for (int i = 0, len = vv.size(); i < len; ++i){ s << vv[i] << std::endl; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::set<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::multiset<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2>& m) {
		s << "{" << std::endl; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << std::endl; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) { 
		return s << "(" << p.first << ", " << p.second << ")"; }
	#define vector dvector
	#define bool dbool
	class SIGFPE_exception : std::exception {};
	class SIGSEGV_exception : std::exception {};
	void catch_SIGFPE(int e) { std::cerr << boost::stacktrace::stacktrace() << std::endl; throw SIGFPE_exception();	}
	void catch_SIGSEGV(int e) { std::cerr << boost::stacktrace::stacktrace() << std::endl; throw SIGSEGV_exception(); }
	signed convertedmain();
	signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
	#define main() convertedmain()
#endif
//#define int long long
using ll = long long;
//constexpr int INF = 1e9;//INT_MAX=(1<<31)-1=2147483647
constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807
constexpr ll MOD = (ll)1e9 + 7;
constexpr double EPS = 1e-9;
constexpr int dx[4] = {1, 0, -1, 0};
constexpr int dy[4] = {0, 1, 0, -1};
constexpr int dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr int dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1};
#define rep(i, n)   for(ll i=0, i##_length=(n); i< i##_length; ++i)
#define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i)
#define rrep(i, n)   for(ll i=(n)-1; i>=0; --i)
#define rrepeq(i, n) for(ll i=(n)  ; i>=1; --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
void p() { std::cout << '\n'; }
template<typename Head, typename... Tail> void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template<typename T> inline void pv(vector<T> &v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template<typename T> inline T gcd(T a, T b) { return b ? gcd(b,a%b) : a; }
template<typename T> inline T lcm(T a, T b) { return a / gcd(a,  b) * b; }
template<typename T> inline bool chmax(T &a, T b) { return a < b && (a = b, true); }
template<typename T> inline bool chmin(T &a, T b) { return a > b && (a = b, true); }
template<typename T> inline void uniq(vector<T> &v) { v.erase(unique(v.begin(), v.end()), v.end()); }

/*-----8<-----template-----8<-----*/
template< typename flow_t >
class FordFulkerson {
public:
	class edge {
		public:
		ll to;
		flow_t cap;
		ll rev;
		bool isrev;
		ll idx;
	};

	vector< vector< edge > > graph;
	vector< ll > used;
	const flow_t INF;
	ll timestamp;

	FordFulkerson(ll n) : INF(numeric_limits< flow_t >::max()), timestamp(0) {
		graph.resize(n);
		used.assign(n, -1);
	}

	void add_edge(ll from, ll to, flow_t cap, ll idx = -1) {
		graph[from].emplace_back((edge) {to, cap, (ll) graph[to].size(), false, idx});
		graph[to].emplace_back((edge) {from, 0, (ll) graph[from].size() - 1, true, idx});
	}

	flow_t dfs(ll idx, const ll t, flow_t flow) {
		if(idx == t) return flow;
		used[idx] = timestamp;
		for(auto &e : graph[idx]) {
			if(e.cap > 0 && used[e.to] != timestamp) {
				flow_t d = dfs(e.to, t, min(flow, e.cap));
				if(d > 0) {
					e.cap -= d;
					graph[e.to][e.rev].cap += d;
					return d;
				}
			}
		}
		return 0;
	}

	flow_t max_flow(ll s, ll t) {
		flow_t flow = 0;
		for(flow_t f; (f = dfs(s, t, INF)) > 0; timestamp++) {
			flow += f;
		}
		return flow;
	}

	void output() {
		for(ll i = 0; i < graph.size(); i++) {
			for(auto &e : graph[i]) {
				if(e.isrev) continue;
				auto &rev_e = graph[e.to][e.rev];
				cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << e.cap + rev_e.cap << ")" << endl;
			}
		}
	}
};
/*-----8<-----library-----8<-----*/


void solve() {
	ll H,W;
	cin>>H>>W;
	vector<string> A(H,"");
	rep(i,H)cin>>A[i];

	ll sx,sy,gx,gy;
	rep(i,H)rep(j,W){
		if(A[i][j]=='S'){
			sx=i,sy=j;
		}else if(A[i][j]=='T'){
			gx=i,gy=j;
		}
	}
	if(sx==gx||sy==gy){
		p(-1);return;
	}
	vector<vector<ll>> tate(H);
	rep(i,H){
		rep(j,W){
			if(A[i][j]!='.')tate[i].push_back(j);
		}
	}
	vector<vector<ll>> yoko(W);
	rep(j,W){
		rep(i,H){
			if(A[i][j]!='.')yoko[j].push_back(i);
		}
	}

	FordFulkerson<ll> g(H*W*2);
	rep(i,H)rep(j,W){
		g.add_edge(i*W+j, i*W+j +H*W, 1);
	}
	rep(i,H)rep(j,W){
		if(A[i][j]=='.')continue;
		for(ll y:tate[i]){
			g.add_edge(i*W+j +H*W, i*W+y, 1e5);
			g.add_edge(i*W+y +H*W, i*W+j, 1e5);
		}
		for(ll x:yoko[j]){
			g.add_edge(i*W+j +H*W, x*W+j, 1e5);
			g.add_edge(x*W+j +H*W, i*W+j, 1e5);
		}
		
	}

	ll ans=g.max_flow(sx*W+sy +H*W, gx*W+gy);
	//g.output();
	p(ans);
}

signed main() {
	solve();
	return 0;
}