#include <iostream>
#include <iomanip>
#include <cmath>
#include <algorithm>

typedef long long ll;
typedef double lf;

// #define DEBUG 1
struct IO
{
    #define MAXSIZE (1 << 20)
    #define isdigit(x) (x >= '0' && x <= '9')
    char buf[MAXSIZE], *p1, *p2;
    char pbuf[MAXSIZE], *pp;
    #if DEBUG
    #else
    IO() : p1(buf), p2(buf), pp(pbuf) {}
    ~IO() {fwrite(pbuf, 1, pp - pbuf, stdout);}
    #endif
    #define gc() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, MAXSIZE, stdin), p1 == p2) ? ' ' : *p1++)
    #define blank(x) (x == ' ' || x == '\n' || x == '\r' || x == '\t')

    template <typename T>
    void Read(T &x)
    {
        #if DEBUG
        std::cin >> x;
        #else
        bool sign = 0; char ch = gc(); x = 0;
        for (; !isdigit(ch); ch = gc())
            if (ch == '-') sign = 1;
        for (; isdigit(ch); ch = gc()) x = x * 10 + (ch ^ 48);
        if (sign) x = -x;
        #endif
    }
    void Read(char *s)
    {
        #if DEBUG
        std::cin >> s;
        #else
        char ch = gc();
        for (; blank(ch); ch = gc());
        for (; !blank(ch); ch = gc()) *s++ = ch;
        *s = 0;
        #endif
    }
    void Read(char &c) {for (c = gc(); blank(c); c = gc());}

    void Push(const char &c)
    {
        #if DEBUG
        putchar(c);
        #else
        if (pp - pbuf == MAXSIZE) fwrite(pbuf, 1, MAXSIZE, stdout), pp = pbuf;
        *pp++ = c;
        #endif
    }
    template <typename T>
    void Write(T x)
    {
        if (x < 0) x = -x, Push('-');
        static T sta[35];
        int top = 0;
        do sta[top++] = x % 10, x /= 10; while (x);
        while (top) Push(sta[--top] ^ 48);
    }
    template <typename T>
    void Write(T x, char lst) {Write(x), Push(lst);}
} IO;
#define Read(x) IO.Read(x)
#define Write(x, y) IO.Write(x, y)
#define Put(x) IO.Push(x)

using namespace std;

const int MAXN = 1e4 + 10, MAXM = 2e5 + 10;
const int dx[4] = {-1, 1, 0, 0}, dy[4] = {0, 0, -1, 1};
const int dx2[4] = {1, -1, 0, 0}, dy2[4] = {0, 0, 1, -1};
const lf eps = 1e-9;

int n, m, pb[4], sum[MAXM];
char mp[MAXN][22];

inline int Tr(int i, int j) { return (i - 1) * m + j; }

lf f[MAXM][62], g[MAXM]; int bg[MAXM];
inline lf &F(int x, int y) { return f[x][y - bg[x]]; }

inline void Gauss()
{
    for (int i = 1; i <= n * m; i++)
    {
        int r = min(n * m, i + m), R = min(n * m, i + 2 * m), p = i;
        for (int j = i; j <= r; j++)
            if (fabs(F(j, i)) > fabs(F(p, i))) p = j;
        if (fabs(F(p, i)) < eps) continue;
        if (p != i)
        {
            swap(g[i], g[p]);
            for (int j = i; j <= R; j++)
                swap(F(i, j), F(p, j));
        }
        g[i] /= F(i, i);
        for (int j = R; j >= i; j--) F(i, j) /= F(i, i);
        for (int j = i + 1; j <= r; j++)
        {
            g[j] -= g[i] * F(j, i);
            for (int k = R; k >= i; k--) F(j, k) -= F(i, k) * F(j, i);
        }
    }
    for (int i = n * m; i >= 1; i--)
    {
        if (fabs(F(i, i)) < eps) continue;
        for (int j = max(1, i - 2 * m); j < i; j++)
            g[j] -= g[i] * F(j, i);
    }
}

int main()
{
    // freopen("A.in", "r", stdin);
    // freopen("A.out", "w", stdout);
    #if DEBUG
    #else
    ios::sync_with_stdio(0), cin.tie(0);
    #endif
    Read(m), Read(n);
    for (int i = 0; i < 4; i++) Read(pb[i]);
    for (int i = 1; i <= n; i++) Read(mp[i] + 1);
    int cnt = 0;
    for (int i = 1; i <= m; i++) cnt += (mp[1][i] == '.');
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
            if (mp[i][j] == '.')
            {
                for (int k = 0; k < 4; k++)
                {
                    int x = i + dx[k], y = j + dy[k];
                    if (x < 1 || x > n || y < 1 || y > m || mp[x][y] == 'X') continue;
                    sum[Tr(i, j)] += pb[k];
                }
            }
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
        {
            bg[Tr(i, j)] = max(1, Tr(i - 1, j));
            F(Tr(i, j), Tr(i, j)) = 1;
            if (i == 1 && mp[i][j] == '.') g[Tr(i, j)] = 1.0 / cnt;
            if (mp[i][j] == 'X') continue;
            for (int k = 0; k < 4; k++)
            {
                int x = i + dx2[k], y = j + dy2[k];
                if (x < 1 || x > n || y < 1 || y > m || mp[x][y] != '.') continue;
                F(Tr(i, j), Tr(x, y)) = -(lf)pb[k] / sum[Tr(x, y)];
            }
        }
    Gauss();
    cout << fixed << setprecision(10);
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
            if (mp[i][j] == 'T')
                cout << g[Tr(i, j)] << '\n';
    return 0;
}