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.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Scanner;

public class SpongebobAndSquares {
    static class Num implements Comparable<Num> {
        long n, m;

        Num(long x, long m2) {
            n = x;
            m = m2;
        }

        @Override
        public int compareTo(Num arg0) {
            return Long.compare(n, arg0.n);
        }

        public String toString() {
            return n + " " + m;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long x = sc.nextLong();
        sc.close();
        int maxM = 10000000;
        long n, m;
        long s, ss, tmp1, tmp2;
        StringBuffer ans = new StringBuffer();
        LinkedList<Num> stack = new LinkedList<>();
        for (m = 1; m <= maxM; m++) {
            s = sumN(m);
            ss = sumN2(m);
            tmp1 = x + s * (m + 1) - ss;
            tmp2 = (m + 1) * m - s;
            if (tmp1 % tmp2 == 0) {
                n = (tmp1 / tmp2) - 1;
                if (n < m)
                    continue;
                stack.push(new Num(m, n));
                if (n != m)
                    stack.push(new Num(n, m));
            }
        }
        Collections.sort(stack);
        Num curr;
        long prev = -1;
        int res = 0;
        HashSet<Long> used = new HashSet<>();
        while (!stack.isEmpty()) {
            curr = stack.pop();
            if (curr.n == prev) {
                if (used.contains(curr.m))
                    continue;
                else
                    used.add(curr.m);
            } else {
                prev = curr.n;
                used.clear();
                used.add(curr.m);
            }
            ans.append(curr + "\n");
            res++;
        }
        System.out.print(res + "\n" + ans);
    }

    private static long sumN(long n) {
        return (n * (n + 1)) / 2;
    }

    private static long sumN2(long n) {
        return (n * (n + 1) * (2 * n + 1)) / 6;
    }
}