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.util.List;
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
 *
 * @author awh
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(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, MyScanner in, PrintWriter out) {
            long x = in.nextLong();
            if (x == 1) {
                out.println(1);
                out.println("1 1");
                return;
            }
            long sum = 0;
            long sumSquare = 0;
            long n = x;
            List<Long> res = new ArrayList<>();
            boolean foundEq = false;
            for (long m = 1; m < n; m++) {
                sum += m;
                //long xx = x+(sum-m)*m-sumSquare;
                BigInteger xx = BigInteger.valueOf(x)
                        .add(BigInteger.valueOf((sum - m) * m))
                        .subtract(BigInteger.valueOf(sumSquare));
                if (xx.mod(BigInteger.valueOf(sum)) == BigInteger.ZERO) {
                    n = xx.divide(BigInteger.valueOf(sum)).longValue();
                    res.add(m);
                    res.add(n);
                    foundEq = (n == m);
                }
                if (xx.divide(BigInteger.valueOf(sum)).longValue() + 1 < m) break;
                sumSquare += m * m;
            }
            if (foundEq) {
                out.println(res.size() - 1);
            } else {
                out.println(res.size());
            }
            for (int i = 0; i < res.size(); i += 2) {
                long a = res.get(i);
                long b = res.get(i + 1);
                out.println(a + " " + b);
            }
            for (int i = res.size() - 2; i >= 0; i -= 2) {
                long a = res.get(i);
                long b = res.get(i + 1);
                if (a != b) out.println(b + " " + a);
            }
        }

    }

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    }
}