import java.io.*; import java.util.*; import java.util.concurrent.ThreadLocalRandom; import java.util.function.IntUnaryOperator; import java.util.function.LongUnaryOperator; import java.util.stream.Collectors; public class Main { static boolean isLocal; Random rand = new Random(); In in = new In(System.in); PrintStream out = System.out; long inf = 0x1fffffffffffffffL; int iinf = 0x3fffffff; long startTime; public static final int N = 60; public int D; public static final int H = 1500; public int M; public int J; public char[] grid; public Pos[] ps; public int[] ds; public Pos[] jps; int[] distances; int[][] route; boolean[][] beam = new boolean[60][N * N]; int[] avgWait = new int[N * N]; int[] jid = new int[N * N]; public static final String[] ss = {"M L", "M U", "M R", "M D", "S"}; long solve(int seed) { startTime = System.currentTimeMillis(); in(); distances = new int[(J+3) * (J+3)]; route = new int[(J+3) * (J+3)][]; Arrays.fill(distances, iinf); for (int i = 0; i < M; i++) { for (int d = 0; d < 4; d++) { Pos cur = ps[i]; while (true) { cur = cur.moved((d+2)%4); if (cur == null || grid[cur.z] == '#') { break; } for (int j = 0; j < 60; j += ds[i]) { beam[j][cur.z] = true; } } } } for (int i = 0; i < N * N; i++) { int c = 1; for (int j = 0; j < 60; j++) { if (beam[j][i]) { c++; } else { c = 1; } avgWait[i] += c; } } for (int i = 0; i < J + 3; i++) { calcDist(i); } int tt = 0; int cur = J; BitSet visited = new BitSet(J + 3); visited.set(J + 2); tt = moveTo(J, J+1, tt, visited); visited.clear(J + 2); tt = moveTo(J+1, J+2, tt, visited); debug(totalCost); return 0; } int totalCost = 0; int moveTo(int s, int g, int tt, BitSet visited) { int cur = s; visited.set(s); while (cur != g) { int md = iinf; int mi = -1; for (int i = 0; i < J + 3; i++) { if (visited.get(i)) { continue; } // debug(i, cur, jps[i].dist(jps[g]), distances[cur * (J + 3) + i]); int d = distances[cur * (J + 3) + i] + jps[i].dist(jps[g]) * 50; if (md > d) { md = d; mi = i; } } visited.set(mi); // debug(cur, mi, md, distances[cur * (J + 3) + mi], jps[mi].dist(jps[g]), g); Pos p = jps[cur]; for (int v : route(jps[cur], jps[mi], tt)) { if (v < 4) p = p.moved(v); tt = (tt + 1) % 60; if (beam[tt][p.z]) { totalCost += D; } totalCost++; out.println(ss[v]); } cur = mi; } return tt; } List route(Pos s, Pos g, int tt) { class S { private final Pos p; private final int t; private final int d; public S(Pos p, int t, int d) { this.p = p; this.t = t; this.d = d; } } PriorityQueue queue = new PriorityQueue<>(Comparator.comparingInt(v -> v.d)); queue.add(new S(s, tt, 0)); int[][] dist = new int[60][N * N]; int[][] prev = new int[60][N * N]; for (int i = 0; i < 60; i++) { Arrays.fill(dist[i], iinf); Arrays.fill(prev[i], -1); } dist[tt][s.z] = 0; while (!queue.isEmpty()) { S v = queue.remove(); if (dist[v.t][v.p.z] < v.d) { continue; } if (v.p.z == g.z) { List route = new ArrayList<>(); Pos cur = v.p; int ct = v.t; while (prev[ct][cur.z] != -1) { route.add(prev[ct][cur.z]); if (prev[ct][cur.z] < 4) { cur = cur.moved((prev[ct][cur.z] + 2) % 4); } ct = (ct + 59) % 60; } Collections.reverse(route); return route; } int nt = (v.t + 1) % 60; for (int d = 0; d < 4; d++) { Pos q = v.p.moved(d); if (q == null || grid[q.z] == '#') { continue; } int cost = dist[v.t][v.p.z] + 1 + (beam[nt][q.z] ? D : 0); if (dist[nt][q.z] > cost) { dist[nt][q.z] = cost; prev[nt][q.z] = d; queue.add(new S(q, nt, cost)); } } int cost = dist[v.t][v.p.z] + 1 + (beam[nt][v.p.z] ? D : 0); if (dist[nt][v.p.z] > cost) { dist[nt][v.p.z] = cost; prev[nt][v.p.z] = 4; queue.add(new S(v.p, nt, cost)); } } throw new RuntimeException(); } // void calcDist(int s, int t) { // Deque deque = new ArrayDeque<>(); // deque.add(new Timing(ps[s], t)); // int[] dist = new int[N * N]; // int[] prev = new int[N * N]; // Timing[] prevState = new Timing[N * N]; // Arrays.fill(dist, iinf); // dist[ps[s].z] = 0; // distances[t][s * (M+3) + s] = 0; // route[t][s * (M+3) + s] = new int[0]; // while (!deque.isEmpty()) { // Timing p = deque.removeFirst(); // if (mid[p.p.z] != -1 && mid[p.p.z] != s) { // distances[t][s * (M+3) + mid[p.p.z]] = dist[p.p.z]; // route[t][s * (M+3) + mid[p.p.z]] = new int[dist[p.p.z]]; // int j = dist[p.p.z]; // Timing cur = p; // while (j > 0) { // j--; // route[t][s * (M+3) + mid[p.p.z]][j] = prev[cur.p.z]; // cur = prevState[cur.p.z]; // } // } // int nt = (p.t + 1) % 60; // for (int d = 0; d < 4; d++) { // Pos q = p.p.moved(d); // if (q == null || grid[q.z] == '#' || grid[q.z] == 'E') { // continue; // } // if (beam[q.z][nt]) { // continue; // } // int cost = beam[nt][q.z] ? D : 1; // if (dist[q.z] > dist[p.p.z] + 1 && q.dist(ps[s]) < iinf) { // dist[q.z] = dist[p.p.z] + 1; // prev[q.z] = d; // prevState[q.z] = p; // deque.addLast(new Timing(q, nt)); // } // } // if (dist[p.p.z] > dist[p.p.z] + 1) { // dist[p.p.z] = dist[p.p.z] + 1; // prev[p.p.z] = 5; // prevState[p.p.z] = p; // deque.addLast(new Timing(p.p, nt)); // } // } // } void calcDist(int s) { class S { private final Pos p; private final int d; public S(Pos p, int d) { this.p = p; this.d = d; } } PriorityQueue queue = new PriorityQueue<>(Comparator.comparingInt(v -> v.d)); queue.add(new S(jps[s], 0)); int[] dist = new int[N * N]; Arrays.fill(dist, iinf); dist[jps[s].z] = 0; while (!queue.isEmpty()) { S v = queue.remove(); if (dist[v.p.z] < v.d) { continue; } if (jid[v.p.z] != -1) { distances[s * (J+3) + jid[v.p.z]] = v.d; } for (int d = 0; d < 4; d++) { Pos q = v.p.moved(d); if (q == null || grid[q.z] == '#') { continue; } int cost = dist[v.p.z] + avgWait[q.z]; if (dist[q.z] > cost && q.dist(jps[s]) < iinf) { dist[q.z] = cost; queue.add(new S(q, cost)); } } } } void in() { in.nextInt(); D = in.nextInt(); in.nextInt(); grid = new char[N * N]; int jc = 0; for (int i = 0; i < N; i++) { char[] s = in.nextCharArray(); for (int j = 0; j < N; j++) { grid[i * N + j] = s[j]; if (grid[i * N + j] == 'J') { jc++; } } } M = in.nextInt(); J = jc; jps = new Pos[J + 3]; ps = new Pos[M]; ds = new int[M]; for (int i = 0; i < M; i++) { int y = in.nextInt(); int x = in.nextInt(); int d = in.nextInt(); ps[i] = pos(x, y); ds[i] = d; } jc = 0; Arrays.fill(jid, -1); for (int i = 0; i < N * N; i++) { if (grid[i] == 'S') { jps[J] = pos(i); jid[i] = J; grid[i] = '.'; } else if (grid[i] == 'K') { jps[J + 1] = pos(i); jid[i] = J + 1; grid[i] = '.'; } else if (grid[i] == 'G') { jps[J + 2] = pos(i); jid[i] = J + 2; grid[i] = '.'; } else if (grid[i] == 'J') { jid[i] = jc; jps[jc++] = pos(i); } else if (grid[i] == 'E') { grid[i] = '#'; } } } static Pos pos(int x, int y) { return Pos.instances[y * N + x]; } static Pos pos(int z) { return Pos.instances[z]; } static class Timing { Pos p; int t, z; public Timing(Pos p, int t) { this.p = p; this.t = t; this.z = p.z * 60 + t; } } static class Pos implements Comparable { static Pos[] instances; static Pos[] moved; static { instances = new Pos[N * N]; moved = new Pos[4 * N * N]; for (int i = 0; i < N * N; i++) { instances[i] = new Pos(i % N, i / N, i); } for (int i = 0; i < N * N; i++) { for (int d = 0; d < 4; d++) { // LURD int nx = i % N + (d - 1) % 2; int ny = i / N + (d - 2) % 2; if (0 <= nx && nx < N && 0 <= ny && ny < N) { moved[i * 4 + d] = instances[ny * N + nx]; } } } } final int x, y, z; private Pos(int x, int y, int z) { this.x = x; this.y = y; this.z = z; } Pos moved(int d) { return moved[z * 4 + d]; } int dist(Pos o) { return Math.abs(x - o.x) + Math.abs(y - o.y); } Pos[] neighbors() { Pos[] p = new Pos[4]; int i = 0; if ((p[i] = moved(0)) != null) i++; if ((p[i] = moved(1)) != null) i++; if ((p[i] = moved(2)) != null) i++; if ((p[i] = moved(3)) != null) i++; return i == 4 ? p : Arrays.copyOf(p, i); } @Override public int compareTo(Pos o) { return Integer.compare(z, o.z); } @Override public boolean equals(Object o) { return o instanceof Pos && z == ((Pos)o).z; } @Override public int hashCode() { return z; } @Override public String toString() { return String.format("(%d, %d)", x, y); } } static void debug(Object... args) { if (!isLocal) { return; } if (args == null || args.getClass() != Object[].class) { args = new Object[] {args}; } System.err.println(Arrays.stream(args).map(obj -> { Class clazz = obj == null ? null : obj.getClass(); return clazz == byte[].class ? Arrays.toString((byte[])obj) : clazz == short[].class ? Arrays.toString((short[])obj) : clazz == int[].class ? Arrays.toString((int[])obj) : clazz == long[].class ? Arrays.toString((long[])obj) : clazz == char[].class ? Arrays.toString((char[])obj) : clazz == float[].class ? Arrays.toString((float[])obj) : clazz == double[].class ? Arrays.toString((double[])obj) : clazz == boolean[].class ? Arrays.toString((boolean[])obj) : obj instanceof Object[] ? Arrays.deepToString((Object[])obj) : String.valueOf(obj); }).collect(Collectors.joining(" "))); } long elapsed() { return (long)((System.currentTimeMillis() - startTime) * (isLocal ? 1.7 : 1)); } boolean elapsed(long timeLimit) { return elapsed() >= timeLimit; } public static void main(String[] args) { new Main().solve(0); } static class Random { private long x, y, z, w; Random() { this(ThreadLocalRandom.current().nextLong()); } Random(long seed) { this.x = seed; for (int i = 0; i < 20; i++) { rand(); } } private long rand() { long t = x ^ (x << 11); x = y; y = z; z = w; w = w ^ (w >>> 19) ^ t ^ (t >>> 8); return x & 0x7fffffff; } long next() { return rand() << 31 | rand(); } int next(int n) { return (int)(rand() % n); } int next(int l, int r) { return (int)(rand() % (r - l) + l); } double nextDouble() { return rand() / 2147483647.0; } } static class In { private final BufferedReader reader; private StringTokenizer tokenizer; In(InputStream input) { this.reader = new BufferedReader(new InputStreamReader(input), 0x10000); } String next() { try { while (tokenizer == null || !tokenizer.hasMoreTokens()) { tokenizer = new StringTokenizer(reader.readLine()); } } catch (IOException ignored) { } return tokenizer.nextToken(); } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } double nextDouble() { return Double.parseDouble(next()); } char[] nextCharArray() { return next().toCharArray(); } String[] nextStringArray(int n) { String[] s = new String[n]; for (int i = 0; i < n; i++) { s[i] = next(); } return s; } char[][] nextCharGrid(int n, int m) { char[][] a = new char[n][m]; for (int i = 0; i < n; i++) { a[i] = next().toCharArray(); } return a; } int[] nextIntArray(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) { a[i] = nextInt(); } return a; } int[] nextIntArray(int n, IntUnaryOperator op) { int[] a = new int[n]; for (int i = 0; i < n; i++) { a[i] = op.applyAsInt(nextInt()); } return a; } int[][] nextIntMatrix(int h, int w) { int[][] a = new int[h][w]; for (int i = 0; i < h; i++) { a[i] = nextIntArray(w); } return a; } long[] nextLongArray(int n) { long[] a = new long[n]; for (int i = 0; i < n; i++) { a[i] = nextLong(); } return a; } long[] nextLongArray(int n, LongUnaryOperator op) { long[] a = new long[n]; for (int i = 0; i < n; i++) { a[i] = op.applyAsLong(nextLong()); } return a; } long[][] nextLongMatrix(int h, int w) { long[][] a = new long[h][w]; for (int i = 0; i < h; i++) { a[i] = nextLongArray(w); } return a; } List> nextEdges(int n, int m, boolean directed) { List> res = new ArrayList<>(); for (int i = 0; i < n; i++) { res.add(new ArrayList<>()); } for (int i = 0; i < m; i++) { int u = nextInt() - 1; int v = nextInt() - 1; res.get(u).add(v); if (!directed) { res.get(v).add(u); } } return res; } } }