Problem: There was an epidemic in Monstropolis and all monsters became sick. To recover, all monsters lined up in queue for an appointment to the only doctor in the city.

Soon, monsters became hungry and began to eat each other. 

One monster can eat other monster if its weight is strictly greater than the weight of the monster being eaten, and they stand in the queue next to each other. Monsters eat each other instantly. There are no monsters which are being eaten at the same moment. After the monster A eats the monster B, the weight of the monster A increases by the weight of the eaten monster B. In result of such eating the length of the queue decreases by one, all monsters after the eaten one step forward so that there is no empty places in the queue again. A monster can eat several monsters one after another. Initially there were n monsters in the queue, the i-th of which had weight ai.

For example, if weights are [1, 2, 2, 2, 1, 2] (in order of queue, monsters are numbered from 1 to 6 from left to right) then some of the options are:

  1. the first monster can't eat the second monster because a1 = 1 is not greater than a2 = 2; 
  2. the second monster can't eat the third monster because a2 = 2 is not greater than a3 = 2; 
  3. the second monster can't eat the fifth monster because they are not neighbors; 
  4. the second monster can eat the first monster, the queue will be transformed to [3, 2, 2, 1, 2]. 



After some time, someone said a good joke and all monsters recovered. At that moment there were k (k ≤ n) monsters in the queue, the j-th of which had weight bj. Both sequences (a and b) contain the weights of the monsters in the order from the first to the last.

You are required to provide one of the possible orders of eating monsters which led to the current queue, or to determine that this could not happen. Assume that the doctor didn't make any appointments while monsters were eating each other.

Input

The first line contains single integer n (1 ≤ n ≤ 500) — the number of monsters in the initial queue.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the initial weights of the monsters.

The third line contains single integer k (1 ≤ k ≤ n) — the number of monsters in the queue after the joke. 

The fourth line contains k integers b1, b2, ..., bk (1 ≤ bj ≤ 5·108) — the weights of the monsters after the joke. 

Monsters are listed in the order from the beginning of the queue to the end.

Output

In case if no actions could lead to the final queue, print "NO" (without quotes) in the only line. 

Otherwise print "YES" (without quotes) in the first line. In the next n - k lines print actions in the chronological order. In each line print x — the index number of the monster in the current queue which eats and, separated by space, the symbol 'L' if the monster which stays the x-th in the queue eats the monster in front of him, or 'R' if the monster which stays the x-th in the queue eats the monster behind him. After each eating the queue is enumerated again. 

When one monster eats another the queue decreases. If there are several answers, print any of them.

Examples

Input

6
1 2 2 2 1 2
2
5 5


Output

YES
2 L
1 R
4 L
3 L


Input

5
1 2 3 4 5
1
15


Output

YES
5 L
4 L
3 L
2 L


Input

5
1 1 1 3 3
3
2 1 6


Output

NO

Note

In the first example, initially there were n = 6 monsters, their weights are [1, 2, 2, 2, 1, 2] (in order of queue from the first monster to the last monster). The final queue should be [5, 5]. The following sequence of eatings leads to the final queue:

  * the second monster eats the monster to the left (i.e. the first monster), queue becomes [3, 2, 2, 1, 2]; 
  * the first monster (note, it was the second on the previous step) eats the monster to the right (i.e. the second monster), queue becomes [5, 2, 1, 2]; 
  * the fourth monster eats the mosnter to the left (i.e. the third monster), queue becomes [5, 2, 3]; 
  * the finally, the third monster eats the monster to the left (i.e. the second monster), queue becomes [5, 5]. 



Note that for each step the output contains numbers of the monsters in their current order in the queue.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.util.Random;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Rustam Musin (PloadyFree@gmail.com)
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        private int n;
        private Treap a;
        private int k;
        private int[] last;
        private List<IntIntPair> ans = new ArrayList<>();

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.readInt();
            a = new Treap(in.readInt());
            for (int i = 1; i < n; i++) {
                a = a.add(in.readInt());
            }
            k = in.readInt();
            last = IOUtils.readIntArray(in, k);
            for (int i = 0; i < k; i++) {
                if (i < a.size && a.get(i) != last[i]) {
                    if (!tryRemove(i, last[i])) {
                        out.print("NO");
                        return;
                    }
                }
            }
            if (a.size != k) {
                out.print("NO");
                return;
            }
            for (int i = 0; i < k; i++) {
                if (a.get(i) != last[i]) {
                    out.print("NO");
                    return;
                }
            }
            out.printLine("YES");
            for (IntIntPair p : ans) {
                out.printLine(p.first + 1 + " " + (p.second == -1 ? "L" : "R"));
            }
        }

        private boolean tryRemove(int from, int need) {
            int have = a.get(from);
            int lastIdx = from;
            while (have < need && ++lastIdx < a.size) {
                have += a.get(lastIdx);
            }
            if (have != need || !hasDistinct(from, lastIdx)) {
                return false;
            }
            int maxElem = max(from, lastIdx);
            int maxIndex = from;
            if (a.get(from) == maxElem) {
                while (a.get(maxIndex + 1) == maxElem) {
                    maxIndex++;
                }
                for (int i = maxIndex; i < lastIdx; i++) {
                    eatAfter(maxIndex);
                }
                for (int i = maxIndex; i > from; i--) {
                    eatBefore(i);
                }
            } else {
                while (a.get(maxIndex) != maxElem) {
                    maxIndex++;
                }
                for (int i = maxIndex; i > from; i--) {
                    eatBefore(i);
                }
                for (int i = maxIndex; i < lastIdx; i++) {
                    eatAfter(from);
                }
            }
            return true;
        }

        private void eatAfter(int index) {
            ans.add(IntIntPair.makePair(index, 1));
            int newValue = a.get(index) + a.get(index + 1);
            a = a.remove(index + 1);
            a = a.set(index, newValue);
        }

        private void eatBefore(int index) {
            ans.add(IntIntPair.makePair(index, -1));
            int newValue = a.get(index - 1) + a.get(index);
            a = a.remove(index);
            a = a.set(index - 1, newValue);
        }

        private boolean hasDistinct(int from, int toInc) {
            int min = a.get(from);
            int max = a.get(toInc);
            for (int i = from; i <= toInc; i++) {
                min = Math.min(min, a.get(i));
                max = Math.max(max, a.get(i));
                if (min != max) {
                    return true;
                }
            }
            return false;
        }

        private int max(int from, int toInc) {
            int max = a.get(from);
            for (int i = from; i <= toInc; i++) {
                max = Math.max(max, a.get(i));
            }
            return max;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class Treap {
        private static final Random rnd = new Random(239);
        public final int value;
        private final long priority;
        private final Treap left;
        private final Treap right;
        public final int size;

        public Treap(int value) {
            this(value, rnd.nextLong(), null, null);
        }

        public Treap(int value, long priority, Treap left, Treap right) {
            this.value = value;
            this.priority = priority;
            this.left = left;
            this.right = right;
            this.size = 1 + getSize(left) + getSize(right);
        }

        public Treap set(int at, int value) {
            Treap.Split split = split(at);
            Treap.Split split1 = split.right.split(1);
            return merge(split.left, merge(new Treap(value), split1.right));
        }

        public int get(int at) {
            int leftSize = getSize(left);
            if (leftSize == at) {
                return value;
            }
            if (leftSize > at) {
                return left.get(at);
            }
            return right.get(at - (leftSize + 1));
        }

        public Treap add(int val) {
            return merge(this, new Treap(val));
        }

        public Treap remove(int at) {
            Treap.Split split = split(at);
            Treap.Split split1 = split.right.split(1);
            return merge(split.left, split1.right);
        }

        private Treap.Split split(int size) {
            int leftSize = getSize(left) + 1;
            if (leftSize <= size) {
                Treap.Split split = right == null ? Treap.Split.empty() : right.split(size - leftSize);
                return new Treap.Split(new Treap(value, priority, left, split.left), split.right);
            } else {
                Treap.Split split = left == null ? Treap.Split.empty() : left.split(size);
                return new Treap.Split(split.left, new Treap(value, priority, split.right, right));
            }
        }

        private static Treap merge(Treap l, Treap r) {
            if (l == null) {
                return r;
            }
            if (r == null) {
                return l;
            }
            return l.priority > r.priority
                    ? new Treap(l.value, l.priority, l.left, merge(l.right, r))
                    : new Treap(r.value, r.priority, merge(l, r.left), r.right);
        }

        private static int getSize(Treap t) {
            return t == null ? 0 : t.size;
        }


        public String toString() {
            String s = "";
            if (left != null) {
                s += left + " ";
            }
            s += value;
            if (right != null) {
                s += " " + right;
            }
            return s;
        }

        private static class Split {
            public final Treap left;
            public final Treap right;

            public Split(Treap left, Treap right) {
                this.left = left;
                this.right = right;
            }

            public static Treap.Split empty() {
                return new Treap.Split(null, null);
            }


            public String toString() {
                return "Split{" +
                        "left=" + left +
                        ", right=" + right +
                        '}';
            }

        }

    }

    static class IOUtils {
        public static int[] readIntArray(InputReader in, int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = in.readInt();
            }
            return array;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class IntIntPair implements Comparable<IntIntPair> {
        public final int first;
        public final int second;

        public static IntIntPair makePair(int first, int second) {
            return new IntIntPair(first, second);
        }

        public IntIntPair(int first, int second) {
            this.first = first;
            this.second = second;
        }


        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            IntIntPair pair = (IntIntPair) o;

            return first == pair.first && second == pair.second;
        }


        public int hashCode() {
            int result = first;
            result = 31 * result + second;
            return result;
        }


        public String toString() {
            return "(" + first + "," + second + ")";
        }

        @SuppressWarnings({"unchecked"})
        public int compareTo(IntIntPair o) {
            int value = Integer.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Integer.compare(second, o.second);
        }

    }
}