#include<cstdio>

#include<cstdlib>

#include<cctype>

#include<algorithm>

#include<cstring>

#include<cmath>

#define maxn 200

using namespace std;

inline long long read(){

    long long num=,f=;

    char ch=getchar();

    while(!isdigit(ch)){

        if(ch=='-')    f=-;

        ch=getchar();

    }

    while(isdigit(ch)){

        num=num*+ch-'';

        ch=getchar();

    }

    return num*f;

}

int u[]={,,,-,};

int w[]={,,-,,};

char mp[maxn][maxn];

double p[maxn];

double g[maxn*][maxn];

int pw[maxn];

int n,m,e,h;

int getlens(int x,int len){    return x/pw[len-]%;    }

double f[][][maxn*][];

bool vis[][][maxn*][];

int chan(int x,int len,int nu){

    return x-getlens(x,len)*pw[len-]+nu*pw[len-];

}

void dfs(int x,int y,int state,int blo){

    //printf("%d %d\n",x,y);

    //printf("%d %d %d %d %.3lf\n",x,y,state,blo,f[x][y][state][blo]);

    if(vis[x][y][state][blo])    return;

    if(mp[x][y]=='@'){    f[x][y][state][blo]=;    vis[x][y][state][blo]=;    return;    }

    if(blo==){    f[x][y][state][blo]=;    vis[x][y][state][blo]=;    return;    }

    vis[x][y][state][blo]=;

    double &ans=f[x][y][state][blo];

    for(int i=;i<;++i){

        int nx=x+u[i],ny=y+w[i];

        if(nx<||nx>n||ny<||ny>m||mp[nx][ny]=='#')    continue;

        char c=mp[nx][ny];

        int now=c-'A'+;

        if(c=='.'||c=='$'||c=='@'||(now>=&&now<=e&&getlens(state,now)==)){

            dfs(nx,ny,state,blo);

            ans=max(ans,f[nx][ny][state][blo]);

        }

        //if(now<1||now>e)    continue;

        if(now>=&&now<=e&&getlens(state,now)==){

            dfs(nx,ny,state,blo-);

            ans=max(ans,f[nx][ny][state][blo-]);

        }

        if(now>=&&now<=e&&getlens(state,now)==){

            int sta=chan(state,now,);

            int stb=chan(state,now,);

            dfs(nx,ny,sta,blo-);

            dfs(nx,ny,stb,blo);

            ans=max(ans,g[state][now]*f[nx][ny][sta][blo-]+(1.0-g[state][now])*f[nx][ny][stb][blo]);

        }

    }

    f[x][y][state][blo]=ans;

    return;

}

int main(){

    int sx,sy;

    n=read(),m=read(),e=read(),h=read();

    for(int i=;i<=n;++i){

        scanf("%s",mp[i]+);

        for(int j=;j<=m;++j)

            if(mp[i][j]=='$'){

                sx=i;    sy=j;

            }

    }

    for(int i=;i<(<<e);++i)    p[i]=read();

    int Max=;pw[]=;

    for(int i=;i<=e;++i)    pw[i]=pw[i-]*;

    //printf("%d",Max);

    for(int i=;i<=pw[e];++i){

        int sum=;

        for(int j=;j<(<<e);++j){

            bool flag=;

            for(int k=;k<=e;++k){

                int now=getlens(i,k),ret=(j>>k-)&;

                if(now==)    continue;

                if(now!=ret){

                    flag=;

                    break;

                }

            }

            if(flag)    continue;

            sum+=p[j];

            for(int k=;k<=e;++k){

                if(getlens(i,k)!=||((j>>k-)&)==)    continue;

                g[i][k]+=p[j];

            }

        }

        for(int j=;j<=e;++j)    g[i][j]/=sum;

    }

    dfs(sx,sy,pw[e]-,h);

    printf("%.3lf",f[sx][sy][pw[e]-][h]);

    return ;

}