#include<bits/stdc++.h>
#define ll long long
#define rep(i, l, r) for (int i=l, _=r; i<=_; i++)
#define per(i, l, r) for (int i=l, _=r; i>=_; i--)
using namespace std;
ll read()
{
    ll s=0, t=1; char ch=getchar();
    for (; ch<'0'||ch>'9'; ch=getchar()) if (ch=='-') t=0;
    for (; ch>='0'&&ch<='9'; ch=getchar()) s=s*10+ch-'0';
    return t?s:-s;
}

const int M=2e5+5, dx[4]={-1, 1, 0, 0}, dy[4]={0, 0, -1, 1};
int dr[100];
int n, m, K;

bool a[M];
struct crd{
    int x, y;
    int nm(){return (x-1)*m+y;}
} p[M], tnp[M];
crd go(crd p, int dir){
    int nx=p.x+dx[dir], ny=p.y+dy[dir];
    if (!nx||!ny||nx>n||ny>m||!a[(crd){nx, ny}.nm()]) return p;
    return (crd){nx, ny};
}
int nm(int x, int y) {return (x-1)*m+y;}
struct que{
    crd x; int tn;
} q[M];
int cnt[M], deg[M], tdeg[M], ans[M];
char op[M], ch[M];
void chgp(crd *p, int dir) {
    rep(x, 1, n) rep(y, 1, m) if (a[nm(x, y)])
        p[nm(x, y)]=go(p[nm(x, y)], dir);
}

int main()
{
    #ifndef ONLINE_JUDGE
    freopen("test.in", "r", stdin);
    freopen("test.out", "w", stdout);
    #endif
    dr['U']=0; dr['D']=1; dr['L']=2; dr['R']=3;
    n=read(), m=read(), K=read();
    scanf("%s", op+1);
    rep(i, 1, n) {
        scanf("%s", ch+1);
        rep(j, 1, m) a[nm(i, j)]=ch[j]^48;
    }
    // rep(i, 1, n) rep(j, 1, m) printf("%d%c", a[nm(i, j)], " \n"[j==m]);
    // cerr<<go((crd){1, 1}, 1).x<<" "<<go((crd){1, 1}, 1).y;

    rep(i, 1, n) rep(j, 1, m) if (a[nm(i, j)]) p[nm(i, j)]=tnp[nm(i, j)]=(crd){i, j};
    rep(i, 1, K) chgp(tnp, dr[op[i]]);// init tnp
    rep(i, 1, n*m) if (a[i]) deg[tnp[i].nm()]++;// init deg
    // rep(i, 1, n) rep(j, 1, m) printf("(%d, %d)%c", tnp[nm(i, j)].x, tnp[nm(i, j)].y, " \n"[j==m]);
    memset(ans, 0x3f, sizeof(ans));

    rep(k, 0, K-1) {
        // printf("k=%d\n", k);
        // rep(i, 1, n) rep(j, 1, m) printf("(%d, %d)%c", p[nm(i, j)].x, p[nm(i, j)].y, " \n"[j==m]);
        memcpy(tdeg, deg, sizeof tdeg);
        memset(cnt, 0, sizeof(cnt));
        int l=1, r=0;
        int cur=0, ct=0;
        rep(i, 1, n*m) cnt[p[i].nm()]++;
        rep(i, 1, n) rep(j, 1, m) if (a[nm(i, j)]) {
            cur+=cnt[nm(i, j)]>0;
            if (!deg[nm(i, j)]) q[++r]={(crd){i, j}, 1};//, printf("push %d %d %d\n", i, j, 1);
        }
        while (l<=r) {
            if (q[l].tn!=ct) {
                ans[cur]=min(ans[cur], ct*K+k);
                ct++;
            }
            // printf("pop (%d, %d) %d\n", q[l].x.x, q[l].x.y, q[l].tn);
            crd x=q[l++].x;
            int num=tnp[x.nm()].nm();
            tdeg[num]--;// printf("%d %d %d\n", tnp[x.nm()].x, tnp[x.nm()].y, tdeg[num]);
            if (!tdeg[num]) q[++r]=(que){tnp[x.nm()], ct+1};//printf("push %d %d %d\n", p[x.nm()].x, p[x.nm()].y, ct+1);
            cnt[num=p[x.nm()].nm()]--;
            if (!cnt[num]) cur--;
        }
        ans[cur]=min(ans[cur], ct*K+k);
        chgp(p, dr[op[k+1]]);
    }
    rep(i, 1, n*m) ans[i]=min(ans[i], ans[i-1]);
    rep(i, 1, n*m) printf("%d\n", ans[i]>1e9?-1:ans[i]);
}