This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
#pragma GCC optimize("Ofast")
typedef int ll;
ll dx[]={1, 0, -1, 0};
ll dy[]={0, 1, 0, -1};
char cad[505][505];
string s;
pair<ll,ll> d(char car)
{
    if(car=='N')
        return {1,0};
    if(car=='S')
        return {-1,0};
    if(car=='W')
        return {0,1};
    if(car=='E')
        return {0,-1};
}
vector<vector<unordered_map<ll,ll>>> mapa;
ll sol(ll px, ll py, ll p)
{
    if(cad[px][py]=='#') return -1;
    if(p==s.size()) return 1;
    if(mapa[px][py][p]!=0) return mapa[px][py][p];
    if(s[p]!='?')
    {
        pair<ll,ll> car=d(s[p]);
        return mapa[px][py][p]=sol(car.first+px,py+car.second,p+1);
    }
    ll bs=-1;
    for(int i=0; i<4; i++){
        bs=max(bs,sol(px+dx[i],py+dy[i],p+1));
        if(bs==1) break;
    }
    return mapa[px][py][p] = bs;
}
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    ll n,m,k;
    cin>>n>>m>>k;
    for(int i=0; i<=n+2; i++)
        for(int j=0;j<=m+2; j++)
            cad[i][j]='#';
 
    for(int i=1; i<=n; i++)
        for(int j=1; j<=m; j++)
            cin>>cad[i][j];
    mapa.assign(505,vector<unordered_map<ll,ll>>(505));
    cin>>s;
    reverse(s.begin(),s.end());
    ll cont=0;
    for(int i=1; i<=n; i++)
    {
        for(int j=1; j<=m; j++)
        {
            cont+=max(sol(i,j,0),0);
        }
    }
    cout<<cont;
    return 0;
}
Compilation message (stderr)
nautilus.cpp: In function 'll sol(ll, ll, ll)':
nautilus.cpp:24:9: warning: comparison of integer expressions of different signedness: 'll' {aka 'int'} and 'std::__cxx11::basic_string<char>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   24 |     if(p==s.size()) return 1;
      |        ~^~~~~~~~~~
nautilus.cpp: In function 'std::pair<int, int> d(char)':
nautilus.cpp:19:1: warning: control reaches end of non-void function [-Wreturn-type]
   19 | }
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