#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;

#include <iterator>
#include <functional>
#include <utility>
#include <type_traits>

template<class Elem> struct vec;

template<class Iter>
struct seq_view{
    using Ref = typename std::iterator_traits<Iter>::reference;
    using Elem = typename std::iterator_traits<Iter>::value_type;
    Iter a, b;
    Iter begin() const { return a; }
    Iter end() const { return b; }
    int size() const { return (int)(b-a); }
    seq_view(Iter first, Iter last) : a(first), b(last) {}
    seq_view sort() const { std::sort(a, b); return *this; }
    Ref& operator[](int x) const { return *(a+x); }
    template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {
        ret x(size()); for(int i=0; i<size(); i++) x[i] = i;
        x().sort([&](int l, int r){ return f(a[l],a[r]); });
        return x;
    }
    template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }
    template<class ret = vec<Elem>> ret cumsum() const {
        auto res = ret(size() + 1, Elem(0));
        for(int i=0; i<size(); i++) res[i+1] = res[i] + operator[](i);
        return res;
    }
    template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>
    ret rle(F eq = F()) const {
        auto x = ret();
        for(auto& a : (*this)){
            if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;
        } return x;
    }
    template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }
    Iter uni() const { return std::unique(a, b); }
    Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }
    Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }
    int lbi(const Elem& x) const { return lb(x) - a; }
    int ubi(const Elem& x) const { return ub(x) - a; }
    seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }
    template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }
    template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }
    template<class F> Iter when_true_to_false(F f) const {
        if(a == b) return a;
        return std::lower_bound(a, b, *a,
            [&](const Elem& x, const Elem&){ return f(x); });
    }
    seq_view same(Elem x) const { return { lb(x), ub(x) }; }
    template<class F> auto map(F f) const {
        vec<decltype(f(std::declval<const typename Iter::value_type&>()))> r;
        for(auto& x : *this) r.emp(f(x));
        return r;
    }
    Iter max() const { return std::max_element(a, b); }
    Iter min() const { return std::min_element(a, b); }
    template<class F = std::less<Elem>>
    Iter min(F f) const { return std::min_element(a, b, f); }
    seq_view rev() const { std::reverse(a, b); return *this; }
};

template<class Elem>
struct vec {
public:
    using Base = typename std::vector<Elem>;
    using Iter = typename Base::iterator;
    using CIter = typename Base::const_iterator;
    using View = seq_view<Iter>;
    using CView = seq_view<CIter>;

    vec(){}
    explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}
    template <class I2> vec(I2 first, I2 last) : a(first, last) {}
    vec(std::initializer_list<Elem> il) : a(std::move(il)) {}
    vec(Base b) : a(std::move(b)) {}
    operator Base() const { return a; }

    Iter begin(){ return a.begin(); }
    CIter begin() const { return a.begin(); }
    Iter end(){ return a.end(); }
    CIter end() const { return a.end(); }
    int size() const { return a.size(); }
    bool empty() const { return a.empty(); }
    Elem& back(){ return a.back(); }
    const Elem& back() const { return a.back(); }
    vec& sortuni(){ (*this)().sort(); a.erase((*this)().uni(), end()); return *this; }
    vec sortunied(){ vec x = *this; x.sortuni(); return x; }
    Iter operator()(int x){ return a.begin() + x; }
    CIter operator()(int x) const { return a.begin() + x; }
    View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }
    CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }
    View operator()(){ return (*this)(0,size()); }
    CView operator()() const { return (*this)(0,size()); }
    Elem& operator[](int x){ return a[x]; }
    const Elem& operator[](int x) const { return a[x]; }
    Base& operator*(){ return a; }
    const Base& operator*() const { return a; }
    vec& push(Elem args){
        a.push_back(std::move(args));
        return *this;
    }
    template<class... Args>
    vec& emp(Args &&... args){
        a.emplace_back(std::forward<Args>(args) ...);
        return *this;
    }
    template<class Range>
    vec& app(Range& x){ for(auto& v : x){ emp(v); } return *this; }
    Elem pop(){ Elem x = std::move(a.back()); a.pop_back(); return x; }
    void resize(int sz){ a.resize(sz); }
    void reserve(int sz){ a.reserve(sz); }
    bool operator==(const vec& r) const { return a == r.a; }
    bool operator!=(const vec& r) const { return a != r.a; }
    bool operator<(const vec& r) const { return a < r.a; }
    bool operator<=(const vec& r) const { return a <= r.a; }
    bool operator>(const vec& r) const { return a > r.a; }
    bool operator>=(const vec& r) const { return a >= r.a; }
    vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }
    template<class F> vec& filter(F f){
        int p = 0;
        for(auto& x : a) if(f(x)) std::swap(a[p++],x);
        resize(p); return *this;
    }
    vec& operator+=(const vec& r){ return app(r); }
    vec operator+(const vec& r) const { vec x = *this; x += r; return x; }
    vec operator*(int t) const { vec res; while(t--){ res += *this; } return res; }
private: Base a;
};

template<class IStr, class U, class T>
IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }
template<class IStr, class T>
IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }
template<class OStr, class T>
OStr& operator<<(OStr& os, const vec<T>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << v[i];
    } return os;
}
template<class OStr, class U, class T>
OStr& operator<<(OStr& os, const vec<std::pair<U,T>>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << '(' << v[i].first << ',' << v[i].second << ')';
    } return os;
}

void testcase(){
    int H, W, K; cin >> H >> W >> K;
    string Instruct; cin >> Instruct;
    vec<string> G(H); cin >> G;
    int numKangaroo = 0;
    auto Id = vec<int>(W*H,-1);
    auto Idx = [&](int y, int x){ return y * W + x; };
    rep(y,H) rep(x,W) if(G[y][x] == '1') Id[Idx(y,x)] = numKangaroo++;
    vec<int> FG(numKangaroo, -2);
    struct Merger { int t; int u; int v; };
    vec<Merger> mergers; {
        auto Per = Id;
        rep(k,K){
            auto nx = vec<int>(W*H,-1);
            char inst = Instruct[k];
            rep(y,H) rep(x,W) if(Per[Idx(y,x)] >= 0){
                int to = 0;
                if(inst == 'U'){
                    to = (y == 0 || G[y-1][x] == '0') ? Idx(y,x) : Idx(y-1,x);
                } else if(inst == 'D'){
                    to = (y == H-1 || G[y+1][x] == '0') ? Idx(y,x) : Idx(y+1,x);
                } else if(inst == 'L'){
                    to = (x == 0 || G[y][x-1] == '0') ? Idx(y,x) : Idx(y,x-1);
                } else if(inst == 'R'){
                    to = (x == W-1 || G[y][x+1] == '0') ? Idx(y,x) : Idx(y,x+1);
                }
                if(nx[to] != -1){
                    mergers.push({ k+1, nx[to], Per[Idx(y,x)] });
                } else {
                    nx[to] = Per[Idx(y,x)];
                }
            }
            swap(nx, Per);
        }
        //cout << Per << endl;
        rep(i,H*W) if(Per[i] >= 0) FG[Per[i]] = Id[i];
    }
    mergers().rev();
    for(auto [t,u,v] : mergers) FG[v] = FG[u];
    mergers().rev();
    //cout << FG << endl;
    vec<int> dfsBackOrder; {
        vec<int> vis(numKangaroo, 0);
        rep(s,numKangaroo){
            vec<int> que;
            que.push(s);
            vis[s] = 1;
            while(vis[FG[que.back()]] == 0){
                que.push(FG[que.back()]);
                vis[que.back()] = 1;
            }
            que().rev();
            dfsBackOrder.app(que);
        }
    }
    vec<int> height(numKangaroo, 0);
    rep(tt,2) for(int i=numKangaroo-1; i>=0; i--){
        chmax(height[FG[dfsBackOrder[i]]], height[dfsBackOrder[i]] + 1);
        rep(i,numKangaroo) chmax(height[FG[i]], height[i] + 1);
    }
    //cout << height << endl;
    vec<int> ans;
    rep(y,H*W) if(Id[y] == -1) ans.push(0);
    ans.push(0);
    for(auto [t,u,v] : mergers){
        if(height[u] < height[v]) swap(height[u], height[v]);
        rep(c,height[v]+1) ans.push(c * K + t);
    }
    ans().sort();
    while(ans.size() < H*W) ans.push(-1);
    ans().rev();
    for(auto a : ans) cout << a << '\n';
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}