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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 * Created with IntelliJ IDEA.
 * User: Daniil
 * Date: 11/21/15
 * Time: 12:55 PM
 * To change this template use File | Settings | File Templates.
 */
public class Main {

    static long  lastSq = 0;

    public static void main(String[] args) {
        //BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        //String line = null;

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


        List<String> sim = new ArrayList<String>();
        List<String> right = new ArrayList<String>();
        for (long m = 1;; ++ m){
            long pro = ((1 + m) * m) / 2;
            long chis = x + (m * (pro - m)) - (sqSum(m - 1));
            if (chis / pro < m){
                //System.out.println(m);
                break;
            }
            if (chis  % pro == 0){
                if (chis/ pro != m){
                    sim.add(chis / pro + " " + m);
                }
                right.add(m + " " + chis / pro);
            }
        }

        System.out.println(right.size() + sim.size());
        for (String r: right){
            System.out.println(r);
        }

        for (int i = sim.size() - 1; i >= 0; -- i){
            System.out.println(sim.get(i));
        }
    }

    public static long sqSum(long c){
        lastSq = lastSq + (c*c);
        return lastSq;
    }
}