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.util.*;
import java.io.*;

public class d {
    final int N = 3_000_000;

    class pair {
        long x, y;
        pair(long x, long y) {
            this.x = x;
            this.y = y;
        }
    }

    long sumOfSquares(long n) {
        return n * (n + 1) * (2 * n + 1) / 6;
    }

    long sum(long n) {
        return n * (n + 1) / 2;
    }

    long count(long n, long m) {
        long x = Math.min(n, m) - 1, y = sum(Math.min(n, m) - 1);
        return (n * n * m) - (y * m) - (y * n) + sumOfSquares(x);
    }

    private void solve() throws IOException {
        long x = nextLong();
        List<pair> p = new ArrayList<>();
        for (long n = 1l; n <= N; ++n) {
            long y = x + n * (n + 1) * (n - 1) / 6;
            long m = n * (n + 1) / 2;

            if (y > 0 && y % m == 0) {
                m = y / m;
                if (n <= m) {
                    p.add(new pair(n, m));
                    if (n != m) {
                        p.add(new pair(m, n));
                    }
                }
            }
        }

        Collections.sort(p, (a, b) -> Long.compare(a.x, b.x));

        out.println(p.size());
        for (pair q : p) {
            out.println(q.x + " " + q.y);
        }
    }

    static void debug(Object...o) {
        System.err.println(Arrays.deepToString(o));
    }

    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

    String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String s = br.readLine();
            if(s != null) {
                st = new StringTokenizer(s);
            }
        }
        if(st.hasMoreTokens()) {
            return st.nextToken();
        } else {
            return null;
        }
    }

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

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

    String nextLine(){
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }

    private void run() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new d().run();
    }
}