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.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;

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

    static class TaskD {
        public void solve(int testNumber, Reader in, PrintWriter out) {
            long x = in.nl();
            ArrayList<PairLong> ans = new ArrayList<>();
            long first, sec, div;
            for (long i = 1; ; i++) {
                first = i * (i + 1) * (2 * i + 1) / 6;
                if (first > x) {
                    break;
                }
                sec = i * (i + 1) / 2;
                if ((x - first) % sec == 0) {
                    div = (x - first) / sec;
                    ans.add(new PairLong(i, i + div));
                    if (div == 0) {
                        continue;
                    }
                    ans.add(new PairLong(i + div, i));
                }
            }
            Collections.sort(ans, new Comparator<PairLong>() {

                public int compare(PairLong o1, PairLong o2) {
                    if (o1.x < o2.x) {
                        return -1;
                    }
                    if (o1.x > o2.x) {
                        return 1;
                    }
                    if (o1.y < o2.y) {
                        return -1;
                    }
                    if (o1.y > o2.y) {
                        return 1;
                    }
                    return 0;
                }
            });
            out.println(ans.size());
            for (int i = 0; i < ans.size(); i++) {
                out.println(ans.get(i).x + " " + ans.get(i).y);
            }
        }

    }

    static class PairLong {
        public long x;
        public long y;

        public PairLong(long x, long y) {
            this.x = x;
            this.y = y;
        }

        public String toString() {
            return x + " " + y;
        }

    }

    static class Reader {
        private BufferedReader in;
        private StringTokenizer st = new StringTokenizer("");
        private String delim = " ";

        public Reader(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            if (!st.hasMoreTokens()) {
                st = new StringTokenizer(rl());
            }
            return st.nextToken(delim);
        }

        public String rl() {
            try {
                return in.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

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

    }
}