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

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>
#include<string.h>

typedef int32_t flow_type;

const flow_type flow_inf=200;

typedef struct flow_edge{
  int vertex;
  int next;
  flow_type capacity;
} flow_edge;

typedef struct maxFlowGraph{
  flow_edge *edge;
  int *start;
  int vertex_num;
  int pointer;
  int edge_length;
} graph;

graph* newGraph(const int vertex_num){
  graph *g=(graph *)calloc(1,sizeof(graph));
  g->vertex_num=vertex_num;
  const int initial_length=4;
  g->edge=(flow_edge *)calloc(initial_length,sizeof(flow_edge));
  g->start=(int *)calloc(vertex_num,sizeof(int));
  g->pointer=0;
  g->edge_length=initial_length;
  for(int i=0;i<vertex_num;i++) g->start[i]=-1;
  return g;
}

void freeGraph(graph *g){
  free(g->edge);
  free(g->start);
  free(g);
}

void addEdge(graph *g,int from,int to,flow_type capa){
  if(g->pointer==g->edge_length){
    g->edge_length*=2;
    g->edge=(flow_edge *)realloc(g->edge,sizeof(flow_edge)*g->edge_length);
  }
  int p=g->pointer;
  g->edge[p]=(flow_edge){to,g->start[from],capa};
  g->start[from]=p;
  g->edge[p+1]=(flow_edge){from,g->start[to],0};
  g->start[to]=p+1;
  g->pointer+=2;
}

flow_type dinic_dfs(int v,graph *g,int dst,int *level,int *iter,flow_type e){
  if(v==dst) return e;
  flow_type sum=0;
  for(int p=iter[v];p!=-1 && e>0;p=g->edge[p].next,iter[v]=p){
    int u=g->edge[p].vertex;
    flow_type capa=g->edge[p].capacity;
    if(level[u]<=level[v] || capa<=0) continue;
    flow_type f=dinic_dfs(u,g,dst,level,iter,capa<e?capa:e);
    if(f>0){
      g->edge[p].capacity-=f;
      g->edge[p^1].capacity+=f;
      sum+=f;
      e-=f;
    }
  }
  return sum;
}

flow_type dinic(const graph *input_graph,const int src,const int dst){
  const int vertex_num=input_graph->vertex_num;
  const int edge_num=input_graph->pointer;
  graph *g=(graph *)calloc(1,sizeof(graph));
  g->edge=(flow_edge *)malloc(sizeof(flow_edge)*edge_num);
  g->start=(int *)malloc(sizeof(int)*vertex_num);
  memcpy(g->edge,input_graph->edge,sizeof(flow_edge)*edge_num);
  memcpy(g->start,input_graph->start,sizeof(int)*vertex_num);
  int *level=(int *)calloc(vertex_num,sizeof(int));
  int *queue=(int *)calloc(vertex_num,sizeof(int));
  int *iter=(int *)calloc(vertex_num,sizeof(int));
  flow_type flow=0;
  while(1){
    memset(level,0,sizeof(int)*vertex_num);
    int front=0,last=0;
    level[src]=1;
    queue[last++]=src;
    while(front<last && level[dst]==0){
      const int v=queue[front++];
      for(int p=g->start[v];p!=-1;p=g->edge[p].next){
	int u=g->edge[p].vertex;
	if(g->edge[p].capacity>0 && level[u]==0){
	  level[u]=level[v]+1;
	  queue[last++]=u;
	}
      }
    }
    if(level[dst]==0) break;
    memcpy(iter,g->start,sizeof(int)*vertex_num);
    while(1){
      flow_type f=dinic_dfs(src,g,dst,level,iter,flow_inf);
      if(f<=0) break;
      flow+=f;
    }
    if (flow >= flow_inf) break;
  }
  freeGraph(g);
  free(level);
  free(queue);
  free(iter);
  return flow;
}

typedef int32_t i32;

void run (void) {
  i32 h, w;
  scanf ("%" SCNi32 "%" SCNi32, &h, &w);
  char *a = (char *) calloc (h * w + 1, sizeof (char));
  for (i32 i = 0; i < h; ++i) {
    scanf ("%s", a + i * w);
  }
  graph *g = newGraph (2 * h * w + 2);
  i32 src = 2 * h * w;
  i32 dst = src + 1;
  for (i32 i = 0; i < h; ++i) {
    for (i32 j = 0; j < w; ++j) {
      if (a[i * w + j] == '.') continue;
      if (a[i * w + j] == 'S') {
	addEdge (g, src, i * w + j, flow_inf);
	addEdge (g, h * w + i * w + j, i * w + j, flow_inf);
      } else if (a[i * w + j] == 'T') {
	addEdge (g, i * w + j, dst, flow_inf);
	addEdge (g, h * w + i * w + j, i * w + j, flow_inf);
      } else {
	addEdge (g, h * w + i * w + j, i * w + j, 1);
      }
      for (i32 k = 0; k < h; ++k) {
	if (k == i || a[k * w + j] == '.') continue;
	addEdge (g, i * w + j, h * w + k * w + j, flow_inf);
      }
      for (i32 k = 0; k < w; ++k) {
	if (k == j || a[i * w + k] == '.') continue;
	addEdge (g, i * w + j, h * w + i * w + k, flow_inf);
      }
    }
  }
  i32 ans = dinic (g, src, dst);
  if (ans >= flow_inf) {
    puts("-1");
  } else {
    printf ("%" PRIi32 "\n",ans);
  }
}

int main (void) {
  run ();
  return 0;
}