Problem: Bob has a simple undirected connected graph (without self-loops and multiple edges). He wants to learn whether his graph is bipartite (that is, you can paint all vertices of the graph into two colors so that there is no edge connecting two vertices of the same color) or not. As he is not very good at programming, he asked Alice for help. He does not want to disclose his graph to Alice, but he agreed that Alice can ask him some questions about the graph.

The only question that Alice can ask is the following: she sends s — a subset of vertices of the original graph. Bob answers with the number of edges that have both endpoints in s. Since he doesn't want Alice to learn too much about the graph, he allows her to ask no more than 20000 questions. Furthermore, he suspects that Alice might introduce false messages to their communication channel, so when Alice finally tells him whether the graph is bipartite or not, she also needs to provide a proof — either the partitions themselves or a cycle of odd length.

Your task is to help Alice to construct the queries, find whether the graph is bipartite. 

Input

The first line contains a single integer n (1 ≤ n ≤ 600) — the number of vertices in Bob's graph.

Interaction

First, read an integer n (1≤ n≤ 600) — the number of vertices in Bob's graph.

To make a query, print two lines. First of which should be in the format "? k" (1 ≤ k ≤ n), where k is the size of the set to be queried. The second line should contain k space separated distinct integers s_1, s_2, ..., s_k (1 ≤ s_i ≤ n) — the vertices of the queried set.

After each query read a single integer m (0 ≤ m ≤ (n(n-1))/(2)) — the number of edges between the vertices of the set \\{s_i\}.

You are not allowed to ask more than 20000 queries.

If m = -1, it means that you asked more queries than allowed, or asked an invalid query. Your program should immediately terminate (for example, by calling exit(0)). You will receive Wrong Answer; it means that you asked more queries than allowed, or asked an invalid query. If you ignore this, you can get other verdicts since your program will continue to read from a closed stream.

After printing a query do not forget to print end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.



When you know the answer, you need to print it.

The format of the answer depends on whether the graph is bipartite or not.

If the graph is bipartite, print two lines. The first should contain the letter "Y" (short for "YES") followed by a space, and then a single integer s (0 ≤ s ≤ n) — the number of vertices in one of the partitions. Second line should contain s integers a_1, a_2, ..., a_s — vertices belonging to the first partition. All a_i must be distinct, and all edges in the main graph must have exactly one endpoint in the set \\{a_i\}.

If the graph is not bipartite, print two lines. The first should contain the letter "N" (short for "NO") followed by a space, and then a single integer l (3 ≤ l ≤ n) — the length of one simple cycle of odd length. Second line should contain l integers c_1, c_2, ..., c_l — the vertices along the cycle. It must hold that for all 1 ≤ i ≤ l, there is an edge \\{c_i, c_{(i mod l)+1}\} in the main graph, and all c_i are distinct.

If there are multiple possible answers, you may print any of them.

Hacks format For hacks, use the following format:

The first line contains two integers n and m~(1 ≤ n ≤ 600, 0 ≤ m ≤ (n(n-1))/(2)) — the number of vertices and edges of the graph, respectively.

Each of the next m lines contains two integers u_i and v_i~(1 ≤ u_i, v_i ≤ n) mean that there is an edge between u_i and v_i. There must not be any multiple edges, no loops, and the graph must be connected.

For example, you need to use this test to get the first sample:
    
    
      
    4 4  
    4 1  
    1 3  
    3 2  
    2 4  
    

Examples

Input

4
4
0
1
1
1
0

Output

? 4 
1 2 3 4
? 2
1 2
? 2
1 3
? 2
1 4
? 2
2 4
? 2
3 4
Y 2
1 2

Input

4
4
3

Output

? 4
1 4 2 3
? 3
1 2 4
N 3
2 1 4

Note

In the first case, Alice learns that there are 4 edges in the whole graph. Over the course of the next three queries, she learns that vertex 1 has two neighbors: 3 and 4. She then learns that while vertex 2 is adjacent to 4, the vertex 3 isn't adjacent to 4. There is only one option for the remaining edge, and that is (2, 3). This means that the graph is a cycle on four vertices, with (1, 2) being one partition and (3, 4) being the second. Here, it would be also valid to output "3 4" on the second line.

In the second case, we also have a graph on four vertices and four edges. In the second query, Alice learns that there are three edges among vertices (1, 2, 4). The only way this could possibly happen is that those form a triangle. As the triangle is not bipartite, Alice can report it as a proof. Notice that she does not learn where the fourth edge is, but she is able to answer Bob correctly anyway.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Collection;
import java.io.IOException;
import java.util.Deque;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            EHiddenBipartiteGraph solver = new EHiddenBipartiteGraph();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class EHiddenBipartiteGraph {
        FastInput in;
        FastOutput out;
        Node[] nodes;
        List<Node> buf = new ArrayList<>(600);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            this.in = in;
            this.out = out;

            int n = in.readInt();

            nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
                nodes[i].id = i;
            }

            for (int i = 1; i < n; i++) {
                dac(0, i - 1, i);
            }

            for (Node node : nodes) {
                paint(node, 0);
            }

            List<Node> black = new ArrayList<>(n);
            for (Node node : nodes) {
                if (node.find() != node) {
                    continue;
                }
                List<Node>[] lists = new ArrayList[]{new ArrayList<>(), new ArrayList<>()};
                for (Node next : node.all) {
                    lists[next.color].add(next);
                }
                black.addAll(lists[0]);

                for (List<Node> list : lists) {
                    if (query(list) == 0) {
                        continue;
                    }
                    int first = 0;
                    while (query(list.subList(first + 1, list.size())) != 0) {
                        first++;
                    }
                    int second = first + 1;
                    while (query(list.get(first), list.get(second)) == 0) {
                        second++;
                    }
                    Deque deque = new ArrayDeque(n);
                    findPathBetween(list.get(first), null, list.get(second), deque);
                    outputLoop(deque);
                    return;
                }
            }

            outputBipartite(black);
        }

        public void paint(Node root, int color) {
            if (root.color != -1) {
                return;
            }
            root.color = color;
            for (Node node : root.next) {
                paint(node, color ^ 1);
            }
        }

        public void dac(int l, int r, int x) {
            int total = query(l, r, x);
            for (int i = l; i <= r; i++) {
                if (nodes[i].find() != nodes[i]) {
                    continue;
                }
                total -= nodes[i].edgeCnt;
            }
            if (total == 0) {
                return;
            }
            if (l == r) {
                int near = find(l, x);
                nodes[near].next.add(nodes[x]);
                nodes[x].next.add(nodes[near]);
                Node.merge(nodes[near], nodes[x]);
                nodes[x].find().edgeCnt += total;
                //System.err.printf("add edge(%d,%d)\n", near + 1, x + 1);
                return;
            }
            int m = (l + r) / 2;
            dac(l, m, x);
            dac(m + 1, r, x);
        }

        public boolean findPathBetween(Node root, Node p, Node target, Deque<Node> deque) {
            deque.addLast(root);
            if (root == target) {
                return true;
            }
            for (Node node : root.next) {
                if (node == p) {
                    continue;
                }
                if (findPathBetween(node, root, target, deque)) {
                    return true;
                }
            }
            deque.removeLast();
            return false;
        }

        public int find(int which, int x) {
            int l = 0;
            int r = nodes[which].all.size() - 1;
            while (l < r) {
                int m = (l + r) / 2;
                List<Node> left = nodes[which].all.subList(l, m + 1);
                if (query(left, nodes[x]) > query(left)) {
                    r = m;
                } else {
                    l = m + 1;
                }
            }
            return nodes[which].all.get(l).id;
        }

        public int query() {
            if (buf.size() <= 1) {
                return 0;
            }

            out.append("? ").append(buf.size()).println();
            for (Node node : buf) {
                out.append(node.id + 1).append(' ');
            }
            out.println().flush();
            return in.readInt();
        }

        public int query(List<Node> nodes) {
            buf.clear();
            buf.addAll(nodes);
            return query();
        }

        public int query(List<Node> nodes, Node x) {
            buf.clear();
            buf.addAll(nodes);
            buf.add(x);
            return query();
        }

        public int query(Node a, Node b) {
            buf.clear();
            buf.add(a);
            buf.add(b);
            return query();
        }

        public int query(int l, int r, int x) {
            buf.clear();
            for (int i = l; i <= r; i++) {
                if (nodes[i].find() != nodes[i]) {
                    continue;
                }
                buf.addAll(nodes[i].all);
            }
            buf.add(nodes[x]);

            return query();
        }

        public void outputLoop(Collection<Node> deque) {
            out.append("N ").append(deque.size()).println();
            for (Node node : deque) {
                out.append(node.id + 1).append(' ');
            }
            out.flush();
        }

        public void outputBipartite(List<Node> list) {
            out.append("Y ").append(list.size()).println();
            for (Node node : list) {
                out.append(node.id + 1).append(' ');
            }
            out.flush();
        }

    }

    static class Node {
        int id;
        List<Node> next = new ArrayList<>();
        int color = -1;
        int edgeCnt;
        Node p = this;
        int rank;
        List<Node> all = new ArrayList<>();

        {
            all.add(this);
        }

        public Node find() {
            return p.p == p ? p : (p = p.find());
        }

        public static void merge(Node a, Node b) {
            a = a.find();
            b = b.find();
            if (a == b) {
                return;
            }
            if (a.rank == b.rank) {
                a.rank++;
            }
            if (a.rank < b.rank) {
                Node tmp = a;
                a = b;
                b = tmp;
            }
            b.p = a;
            a.all = CollectionUtils.mergeHeuristically(a.all, b.all);
            a.edgeCnt += b.edgeCnt;
        }

    }

    static class CollectionUtils {
        public static <E, T extends Collection<E>> T mergeHeuristically(T a, T b) {
            if (a.size() >= b.size()) {
                a.addAll(b);
                return a;
            } else {
                b.addAll(a);
                return b;
            }
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            return this;
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}