Problem: Fox Ciel wants to write a task for a programming contest. The task is: "You are given a simple undirected graph with n vertexes. Each its edge has unit length. You should calculate the number of shortest paths between vertex 1 and vertex 2."

Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to k?

Input

The first line contains a single integer k (1 ≤ k ≤ 109).

Output

You should output a graph G with n vertexes (2 ≤ n ≤ 1000). There must be exactly k shortest paths between vertex 1 and vertex 2 of the graph.

The first line must contain an integer n. Then adjacency matrix G with n rows and n columns must follow. Each element of the matrix must be 'N' or 'Y'. If Gij is 'Y', then graph G has a edge connecting vertex i and vertex j. Consider the graph vertexes are numbered from 1 to n.

The graph must be undirected and simple: Gii = 'N' and Gij = Gji must hold. And there must be at least one path between vertex 1 and vertex 2. It's guaranteed that the answer exists. If there multiple correct answers, you can output any of them. 

Examples

Input

2

Output

4
NNYY
NNYY
YYNN
YYNN

Input

9

Output

8
NNYYYNNN
NNNNNYYY
YNNNNYYY
YNNNNYYY
YNNNNYYY
NYYYYNNN
NYYYYNNN
NYYYYNNN

Input

1

Output

2
NY
YN

Note

In first example, there are 2 shortest paths: 1-3-2 and 1-4-2.

In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2.

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.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Collections;
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);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        List<List<Integer>> g = new ArrayList<>();

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int k = in.readInt();
//        k = (1 << 29) - 1;

            if (k == 1) {
                out.print("2\n" +
                        "NY\n" +
                        "YN\n");
                return;
            }

            int len = Integer.toBinaryString(k).length();
            List<Integer> mainLine = new ArrayList<>();
            for (int i = 0; i < len; i++) {
                mainLine.add(create());
            }
            Collections.swap(mainLine, 1, mainLine.size() - 1);
            for (int i = 0; i < len - 1; i++) {
                int left = mainLine.get(i);
                int right = mainLine.get(i + 1);
                int u = create();
                int v = create();
                add(left, u);
                add(u, right);
                add(left, v);
                add(v, right);
                if (((k >> (len - 2 - i)) & 1) == 1) {
                    int prev = mainLine.get(0);
                    for (int j = 0; j < i * 2 + 1; j++) {
                        int next = create();
                        add(prev, next);
                        prev = next;
                    }
                    add(prev, right);
                }
            }
            int n = g.size();
            boolean[][] graph = new boolean[n][n];
            for (int i = 0; i < n; i++) {
                for (int to : g.get(i)) {
                    graph[i][to] = true;
                }
            }
            out.printLine(n);
            for (int i = 0; i < n; i++, out.printLine()) {
                for (int j = 0; j < n; j++) {
                    out.print(graph[i][j] ? 'Y' : 'N');
                }
            }

            if (false) {
                for (int i = 0; i < n; i++, out.printLine()) {
                    out.print(i + 1 + ":");
                    for (int to : get(i)) {
                        out.print(" " + ++to);
                    }
                }
            }
        }

        int create() {
            g.add(new ArrayList<>());
            return g.size() - 1;
        }

        List<Integer> get(int v) {
            if (g.size() == v) {
                g.add(new ArrayList<>());
            }
            return g.get(v);
        }

        void add(int u, int v) {
            get(u).add(v);
            get(v).add(u);
        }

    }

    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() {
            writer.println();
        }

        public void print(char i) {
            writer.print(i);
        }

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

        public void printLine(int i) {
            writer.println(i);
        }

    }

    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);

        }

    }
}