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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

type Weight = i32;
#[allow(dead_code)]
#[derive(Clone, Debug, Eq, PartialEq)]
struct Edge {
    index: usize,
    src: usize,
    dest: usize,
    weight: Weight,
}
#[allow(dead_code)]
impl Edge {
    fn new(index: usize, src: usize, dest: usize, weight: Weight) -> Edge {
        Edge {
            index: index,
            src: src,
            dest: dest,
            weight: weight,
        }
    }
}
impl std::cmp::Ord for Edge {
    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
        (self.weight, self.src, self.dest).cmp(&(other.weight, other.src, other.dest))
    }
}
impl std::cmp::PartialOrd for Edge {
    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
        Some(self.cmp(other))
    }
}
type Edges = Vec<Edge>;
type Graph = Vec<Edges>;
#[allow(dead_code)]
fn graph_new(n: usize) -> Graph {
    vec![vec![]; n]
}
use std::collections::VecDeque;
// index ^ 1 is reverse edge
#[allow(dead_code)]
fn add_uni_edge(graph: &mut Graph, index: &mut usize, src: usize, dest: usize, weight: Weight) {
    graph[src].push(Edge::new(*index, src, dest, weight));
    *index += 1;
    graph[dest].push(Edge::new(*index, dest, src, 0));
    *index += 1;
}

#[allow(dead_code)]
fn augment(
    g: &Graph,
    capacity: &mut Vec<Weight>,
    level: &Vec<usize>,
    finished: &mut Vec<bool>,
    from: usize,
    t: usize,
    cur: Weight,
) -> Weight {
    if from == t || cur == 0 {
        return cur;
    }
    if finished[from] {
        return 0;
    }
    for edge in g[from].iter() {
        let to = edge.dest;
        if level[to] != level[from] + 1 {
            continue;
        }
        let ncur = std::cmp::min(cur, capacity[edge.index]);
        let f = augment(g, capacity, level, finished, to, t, ncur);
        if f > 0 {
            capacity[edge.index] -= f;
            capacity[edge.index ^ 1] += f;
            return f;
        }
    }
    finished[from] = true;
    0
}

#[allow(dead_code)]
fn max_flow(g: &Graph, e: usize, s: usize, t: usize) -> Weight {
    let n = g.len();
    let mut capacity: Vec<Weight> = vec![0; e];
    for from in 0..n {
        for edge in g[from].iter() {
            capacity[edge.index] += edge.weight;
        }
    }
    let mut ans = 0;
    loop {
        let mut level = vec![usize::max_value(); n];
        level[s] = 0;
        let mut que = VecDeque::<usize>::new();
        que.push_back(s);
        while let Some(from) = que.pop_front() {
            if from == t {
                break;
            }
            for edge in g[from].iter() {
                let to = edge.dest;
                if capacity[edge.index] > 0 && level[to] == usize::max_value() {
                    que.push_back(to);
                    level[to] = level[from] + 1;
                }
            }
        }
        let mut finished = vec![false; n];
        let mut end = true;
        loop {
            let f = augment(
                g,
                &mut capacity,
                &level,
                &mut finished,
                s,
                t,
                Weight::max_value(),
            );
            if f == 0 {
                break;
            }
            ans += f;
            end = false;
        }
        if end {
            break;
        }
    }
    ans
}

fn main() {
    let h = read::<usize>();
    let w = read::<usize>();
    let mut field = vec![vec![]; h];
    for y in 0..h {
        field[y] = read::<String>().chars().collect::<Vec<char>>();
    }
    let in_node = |y: usize, x: usize| y * w + x;
    let out_node = |y: usize, x: usize| y * w + x + h * w;
    let graph_size = || h * w * 2;
    let mut g = graph_new(graph_size());
    let mut e = 0;
    let mut s = 0;
    let mut t = 0;
    for y in 0..h {
        for x in 0..w {
            if field[y][x] == '.' {
                continue;
            }
            if field[y][x] == 'S' {
                s = in_node(y, x);
            }
            if field[y][x] == 'T' {
                t = out_node(y, x);
            }
            add_uni_edge(&mut g, &mut e, out_node(y, x), in_node(y, x), 1);
            for ny in 0..h {
                if y == ny || field[ny][x] == '.' {
                    continue;
                }
                add_uni_edge(&mut g, &mut e, in_node(y, x), out_node(ny, x), 10000);
            }
            for nx in 0..w {
                if x == nx || field[y][nx] == '.' {
                    continue;
                }
                add_uni_edge(&mut g, &mut e, in_node(y, x), out_node(y, nx), 10000);
            }
        }
    }
    let mut ans = max_flow(&g, e, s, t);
    if s % w == t % w || s / w == t / w {
        ans = -1;
    }
    println!("{}", ans);
}