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.ArrayList;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.List;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Collections;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    static class Pair implements Comparable<Pair>{
        public long n,m;

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


        public int compareTo(Pair o) {
            if (n != o.n){
                return ((Long)n).compareTo(o.n);
            }

            return ((Long)m).compareTo(o.m);
        }
    }

    private static final int MAX = 10000000;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        long x = in.nextLong();

        List<Pair> sol = new ArrayList<Pair>();

        for (long n=1; n<=MAX; n++){
            long m = ((6L * x) / (n* (n+1)) + n - 1) / 3;

            if (n*(n+1)*(3*m -n + 1) == 6*x){

                if (n < m){
                    sol.add(new Pair(n, m));
                    sol.add(new Pair(m, n));
                } else if (n == m){
                    sol.add(new Pair(n,m));
                }
            }
        }

        Collections.sort(sol);

        out.println(sol.size());

        for (Pair p: sol){
            out.println(p.n + " " + p.m);
        }
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;


    public InputReader(InputStream stream){
        reader = new BufferedReader(new InputStreamReader(stream));
    }

    public String next(){
        while (tokenizer == null || !tokenizer.hasMoreTokens()){
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException("FATAL ERROR", e);
            }
        }

        return tokenizer.nextToken();
    }

    public long nextLong(){
        return Long.valueOf(next());
    }
}