Problem: Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3 × 5 table there are 15 squares with side one, 8 squares with side two and 3 squares with side three. The total number of distinct squares in a 3 × 5 table is 15 + 8 + 3 = 26.

Input

The first line of the input contains a single integer x (1 ≤ x ≤ 1018) — the number of squares inside the tables Spongebob is interested in.

Output

First print a single integer k — the number of tables with exactly x distinct squares inside.

Then print k pairs of integers describing the tables. Print the pairs in the order of increasing n, and in case of equality — in the order of increasing m.

Examples

Input

26


Output

6
1 26
2 9
3 5
5 3
9 2
26 1


Input

2


Output

2
1 2
2 1


Input

8


Output

4
1 8
2 3
3 2
8 1

Note

In a 1 × 2 table there are 2 1 × 1 squares. So, 2 distinct squares in total.

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In a 2 × 3 table there are 6 1 × 1 squares and 2 2 × 2 squares. That is equal to 8 squares in total.

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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.io.IOException;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Objects;
import java.util.List;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ruins He
 */
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);
    TaskD solver = new TaskD();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskD {
    private static final long BOUND = (long) 2e6;

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      long sum = in.nextLong();
      List<Pair<Long, Long>> res = new ArrayList<>();
      for (long r = 1; r <= BOUND; r++) {
        long x = (6 * sum - r + r * r * r);
        long y = (3 * r * (r + 1));
        if (x > 0 && x % y == 0) {
          long c = x / y;
          if (c < r) continue;
          res.add(Pair.of(r, c));
          if (r != c) res.add(Pair.of(c, r));
        }
      }
      Collections.sort(res);
      out.println(res.size());
      for (Pair<Long, Long> e : res) {
        out.println(e.first + " " + e.second);
      }
    }

  }

  static class OutputWriter {
    private final PrintWriter writer;

    private OutputWriter(Writer writer, boolean autoFlush) {
      this.writer = new PrintWriter(new BufferedWriter(writer, 32767), autoFlush);
    }

    public OutputWriter(Writer writer) {
      this(writer, true);
    }

    public OutputWriter(OutputStream outputStream) {
      this(new OutputStreamWriter(outputStream), false);
    }

    public OutputWriter println(String string) {
      writer.println(string);
      return this;
    }

    public OutputWriter println(int value) {
      writer.println(value);
      return this;
    }

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

  }

  static class Pair<F extends Comparable<F>, S extends Comparable<S>> implements Comparable<Pair<F, S>> {
    public F first;
    public S second;

    public Pair(F first, S second) {
      this.first = first;
      this.second = second;
    }

    public static <F extends Comparable<F>, S extends Comparable<S>> Pair<F, S> of(
        F first, S second) {
      return new Pair<>(first, second);
    }


    public int compareTo(Pair<F, S> other) {
      int fd = this.first.compareTo(other.first);
      if (fd != 0) return fd;
      else return this.second.compareTo(other.second);
    }


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


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

      Pair<?, ?> pair = (Pair<?, ?>) o;

      if (first != null ? !first.equals(pair.first) : pair.first != null) return false;
      return !(second != null ? !second.equals(pair.second) : pair.second != null);

    }


    public int hashCode() {
      return Objects.hash(first, second);
    }

  }

  static class InputReader {
    public final BufferedReader reader;
    public StringTokenizer tokenizer = null;

    public InputReader(Reader reader) {
      this.reader = new BufferedReader(reader, 32767);
    }

    public InputReader(InputStream inputStream) {
      this(new InputStreamReader(inputStream));
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public long nextLong() {
      return Long.parseLong(next());
    }

  }
}