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.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 * Created by leen on 7/25/16.
 */
public class _599D {
    static long[] g = new long[1442251];
    public static void main(String[] args) {

        long current = 0;
        for(int i = 2; i <= 1442250; i++) {
            current +=  (long)i * (long)i;
            g[i] = current;
        }

        Scanner scan = new Scanner(System.in);
        long x = scan.nextLong();

        List<Pair> pairs = new ArrayList<Pair>();
        for(int n = 1; n <= 1442250; n++) {
            long m = solveM(x, n);
            if(m == -1L)
                continue;
            if(m == -2L)
                break;
            pairs.add(new Pair(n, m));
        }

        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out, 1024 * 128));

        Pair lastPair = pairs.get(pairs.size()-1);
        if(lastPair.n == lastPair.m)
            pw.println(pairs.size() * 2 - 1);
        else
            pw.println(pairs.size() * 2);

        for(int i = 0; i < pairs.size(); i++) {
            Pair pair = pairs.get(i);
            pw.println(pair.n + " " + pair.m);
        }

        for(int i = pairs.size() - 1; i >= 0; i--) {
            Pair pair = pairs.get(i);
            if(pair.n != pair.m)
                pw.println(pair.m + " " + pair.n);
        }

        pw.flush();
    }

    static long solveM(long x, long n) {
        long a = (x+n-1 + n*(2+n)*(n-1)/2 - g[(int)n]);
        long b = ((2+n)*(n-1)/2 + 1);
        if(a % b != 0L)
            return -1L;
        if(a / b < n)
            return -2L;
        return a / b;
    }

    static class Pair {
        int n;
        long m;

        Pair(int n, long m) {
            this.n = n;
            this.m = m;
        }
    }
}