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.*;
import java.util.*;
public class D599 {
public static void main(String[] args) throws IOException {
    input.init(System.in);
    PrintWriter out = new PrintWriter(System.out);
    long k = input.nextLong();
    ArrayList<Long> ns = new ArrayList<Long>(), ms = new ArrayList<Long>();
    for(long n = 1; n*n*n <= 3*k; n++)
    {
        long num = 6*k + 3*n*n*n - 3*n*n - n * (n-1) * (2*n-1);
        long denom = 6*n*n - 3*n*(n-1);
        //System.out.println(n+" "+num+" "+denom);
        if(num%denom == 0)
        {
            long m = num/denom;
            if(m >= n)
            {
                ns.add(n);
                ms.add(m);
            }
            if(n != m)
            {
                ns.add(m);
                ms.add(n);
            }
        }
    }
    Collections.sort(ns);
    Collections.sort(ms);
    Collections.reverse(ms);
    out.println(ns.size());
    for(int i = 0; i<ns.size(); i++) out.println(ns.get(i)+" "+ms.get(i));
    out.close();
}

public static class input {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) {
    reader = new BufferedReader(new InputStreamReader(input));
    tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
    while (!tokenizer.hasMoreTokens())
        tokenizer = new StringTokenizer(reader.readLine());
    return tokenizer.nextToken();
    }

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

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

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