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.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class SpongebobAndSquares {

	static final long MAX = (long) 2e6;

	static class Pair {
		long f, s;

		Pair(long a, long b) {
			f = a;
			s = b;
		}

		@Override
		public String toString() {
			return f + " " + s;
		}
	}

	static long cube(long x) {
		return sq(x) * x;
	}

	static long sq(long x) {
		return x * x;
	}

	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		long x = sc.nextLong() * 6;
		ArrayList<Pair> a = new ArrayList<>();
		for (long m = 1; m <= MAX; m++) {
			long num = x + cube(m) - m, den = 3 * (sq(m) + m);
			if (num % den == 0) {
				long n = num / den;
				if (n < m)
					continue;
				a.add(new Pair(n, m));
				if (n != m)
					a.add(new Pair(m, n));
			}
		}
		out.println(a.size());
		Collections.sort(a, (p1, p2) -> {
			if (p1.f != p2.f)
				return Long.compare(p1.f, p2.f);
			return Long.compare(p1.s, p2.s);
		});
		for (int i = 0; i < a.size(); i++) {
			Pair p = a.get(i);
			out.printf("%d %d\n", p.f, p.s);
		}
		out.flush();
		out.close();
	}

	static class MyScanner {
		StringTokenizer st;
		BufferedReader br;

		public MyScanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public MyScanner(String filename) throws IOException {
			br = new BufferedReader(new FileReader(new File(filename)));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}
}