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.LinkedList;
import java.util.Scanner;

public class Solution {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        long x = in.nextLong();
        LinkedList<long[]> s = new LinkedList<long[]>();
        for(int m = 1; m <= Math.min(x, 1e7); m++) {
            long result = fixm(x, m);
            if(result == -1) {
                continue;
            }
            if(result < m) {
                break;
            }
            s.add(new long[]{m,result});
        }
        boolean last = false;
        if(s.size() > 0 && s.getLast()[0] != s.getLast()[1]) {
            last = true;
        }
        System.out.println(2 * s.size() - (last ? 0 : 1));
        for(int i = 0; i < s.size(); i++) {
            System.out.println(s.get(i)[0] + " " + s.get(i)[1]); 
        }
        for(int i = s.size() - 1 - (last ? 0 : 1); i >= 0; i--) {
            System.out.println(s.get(i)[1] + " " + s.get(i)[0]); 
        }
    }
    public static long fixm(long x, long m) {
        // ct + dx * n == x, x - ct / dx
        long ct = (m * (m + 1) * (2 * m + 1)) / 6;
        long dx = (m * (m + 1)) / 2;
        if((x - ct) % dx != 0) {
            return -1;
        }
        return (x - ct) / dx + m;
    }
}