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.PrintWriter;
import java.util.Scanner;
import java.util.TreeSet;

/**
 * Created by omar on 11/11/17.
 */
public class Main {

    static long get (long m, long R) {
        long n = (6L * R + m * m * m - m) / (3 * (m * m + m));
        return n >= m && (m * (m + 1) * (3 * n - m + 1)) / 6 == R ? n : -1;
    }

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        long x = sc.nextLong();
        long upper = 2L * (long)Math.pow(x, 1.0 / 3) + 2;
        TreeSet<Pair> pairs = new TreeSet<>();
        for (int m = 1; m <= upper; m++) {
            long n = get(m, x);
            if (n != -1) {
                pairs.add(new Pair(n, m));
                pairs.add(new Pair(m, n));
            }
        }

        out.println(pairs.size());
        for (Pair p : pairs)
            out.println(p.f + " " + p.s);
        out.flush();
        out.close();
    }
    static class Pair implements Comparable<Pair> {
        long f, s;

        Pair (long ff, long ss) {f = ff; s = ss;}
        @Override
        public int compareTo(Pair pair) {
            return f != pair.f ? Long.compare(f, pair.f) : Long.compare(s, pair.s);
        }
    }
}