#include <bits/stdc++.h>
using namespace std;

int H, W, K;
int Answer[1 << 18];
string C[1 << 18];
string S;

// Other than input
bool Used[1 << 18];
bool Cycle[1 << 18];
int P[1 << 18];
int Dist[1 << 18];
int Count[1 << 18];
vector<int> G[1 << 18];

pair<int, int> Simulation(int px, int py, int cl, int cr) {
	for (int i = cl; i < cr; i++) {
		int idx = (i >= K ? i - K : i);
		if (S[idx] == 'U') {
			if (px >= 1 && C[px - 1][py] == '1') px--;
		}
		if (S[idx] == 'D') {
			if (px <= H - 2 && C[px + 1][py] == '1') px++;
		}
		if (S[idx] == 'L') {
			if (py >= 1 && C[px][py - 1] == '1') py--;
		}
		if (S[idx] == 'R') {
			if (py <= W - 2 && C[px][py + 1] == '1') py++;
		}
	}
	return make_pair(px, py);
}

void dfs(int pos) {
	Dist[pos] = 0;
	for (int to : G[pos]) {
		dfs(to);
		Dist[pos] = max(Dist[pos], Dist[to] + 1);
	}
}

int main() {
	// Step 1. Input
	cin >> H >> W >> K;
	cin >> S;
	for (int i = 0; i < H; i++) cin >> C[i];
	for (int i = 1; i <= H * W; i++) Answer[i] = (1 << 30);

	// Step 2. Brute Force
	for (int i = 0; i < K; i++) {
		for (int j = 0; j <= H * W + 2; j++) Used[j] = false;
		for (int j = 0; j <= H * W + 2; j++) Cycle[j] = false;
		for (int j = 0; j <= H * W + 2; j++) G[j].clear();
		for (int j = 0; j <= H * W + 2; j++) Count[j] = 0;
		for (int j = 0; j < H * W; j++) {
			if (C[j / W][j % W] == '0') continue;
			pair<int, int> x = Simulation(j / W, j % W, 0, i);
			Used[x.first * W + x.second] = true;
		}

		// Make Graph
		int root = 0;
		for (int j = 0; j < H * W; j++) {
			if (Used[j] == false) continue;
			pair<int, int> L = Simulation(j / W, j % W, i, i + K);
			P[j] = L.first * W + L.second;
			root = j;
		}

		// Get Cycles
		int cx = root;
		for (int j = 0; j < 3 * H * W; j++) {
			cx = P[cx];
			if (j >= 2 * H * W) Cycle[cx] = true;
		}
		for (int j = 0; j < H * W; j++) {
			if (Used[j] == false || Cycle[j] == true) continue;
			G[P[j]].push_back(j);
		}

		// Get Distance
		for (int j = 0; j < H * W; j++) {
			if (Cycle[j] == false) continue;
			dfs(j);
		}

		// Get Answer
		for (int j = 0; j < H * W; j++) {
			if (Used[j] == false) continue;
			int dst = Dist[j];
			if (Cycle[j] == true) dst = H * W + 1;
			Count[dst] += 1;
		}
		for (int j = H * W + 1; j >= 1; j--) Count[j - 1] += Count[j];

		// Update Answer
		for (int j = 0; j <= H * W; j++) {
			Answer[Count[j]] = min(Answer[Count[j]], j * K + i);
		}
	}

	// Step 3. Output
	for (int i = 2; i <= H * W; i++) Answer[i] = min(Answer[i], Answer[i - 1]);
	for (int i = 1; i <= H * W; i++) {
		if (Answer[i] == (1 << 30)) printf("-1\n");
		else printf("%d\n", Answer[i]);
	}
	return 0;
}