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.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class BFoxAndMinimalPath {
        int[][] ans;
        int cur;
        int max = 1001;
        int low = 900;
        int high = 950;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            long k = in.readInt();
            ans = new int[max][max];
            for (int i = low; i < high; i++) {
                ans[i][i + 1] = 1;
            }
            ans[high][2] = 1;

            cur = 3;
            for (int i = 0; i <= 30; i++) {
                if (((k >> i) & 1) == 1) {
                    make(1 << i);
                }
            }
            out.println(max - 1);
            for (int i = 1; i < ans.length; i++) {
                for (int j = 1; j < ans.length; j++) {
                    out.print(Math.max(ans[i][j], ans[j][i]) == 1 ? 'Y' : 'N');
                }
                out.println();
            }
        }

        void make(int val) {
            if (val == 1) {
                ans[1][cur] = 1;
                ans[cur][low + 1] = 1;
                cur++;
            } else {
                ans[1][cur] = 1;
                ans[1][cur + 1] = 1;
                cur += 2;
                int layers = 1;
                for (int i = val; i > 2; i /= 2) {
                    ans[cur][cur - 2] = 1;
                    ans[cur][cur - 1] = 1;
                    ans[cur + 1][cur - 2] = 1;
                    ans[cur + 1][cur - 1] = 1;
                    cur += 2;
                    layers++;
                }
                ans[cur - 2][low + layers] = 1;
                ans[cur - 1][low + layers] = 1;
            }
        }

    }

    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);

        }

    }
}