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.

<image>

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

<image>

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
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);
        d599 solver = new d599();
        solver.solve(1, in, out);
        out.close();
    }

    static class d599 {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            long x = in.nextLong();
            ArrayList<Long> hAns = new ArrayList<>();
            ArrayList<Long> wAns = new ArrayList<>();
            long h = 2;
            hAns.add(1L);
            wAns.add(x);
            BigInteger bigX = BigInteger.valueOf(x);
            while (true) {
                BigInteger num = BigInteger.valueOf(6);
                num = num.multiply(bigX);
                num = num.add(BigInteger.valueOf(h).pow(3));
                num = num.subtract(BigInteger.valueOf(h));
                BigInteger den = BigInteger.valueOf(3);
                den = den.multiply(BigInteger.valueOf(h).pow(2).add(BigInteger.valueOf(h)));
                long w = num.divide(den).longValue();
                if (w < h) break;
                if (num.remainder(den).longValue() == 0) {
                    hAns.add(h);
                    wAns.add(w);
                }
                h++;
            }
            if (hAns.get(hAns.size() - 1).equals(wAns.get(wAns.size() - 1))) {
                out.println(2 * hAns.size() - 1);
                for (int i = 0; i < hAns.size(); i++) {
                    out.println(hAns.get(i) + " " + wAns.get(i));
                }
                for (int i = hAns.size() - 2; i >= 0; i--) {
                    out.println(wAns.get(i) + " " + hAns.get(i));
                }
            } else {
                out.println(2 * hAns.size());
                for (int i = 0; i < hAns.size(); i++) {
                    out.println(hAns.get(i) + " " + wAns.get(i));
                }
                for (int i = hAns.size() - 1; i >= 0; i--) {
                    out.println(wAns.get(i) + " " + hAns.get(i));
                }
            }
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public String next() {
            while (stt == null || !stt.hasMoreTokens()) {
                stt = new StringTokenizer(nextLine());
            }
            return stt.nextToken();
        }

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

    }
}