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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;

public class SpongebobAndSquares {
	private static final BufferedReader in = new BufferedReader(
			new InputStreamReader(System.in));
	private static final BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
	
	public void solve() throws IOException {
		long x = Long.parseLong(in.readLine());
		ArrayList<String> r = new ArrayList<String>();
		ArrayList<String> res = new ArrayList<String>();
		long cnt = 0;
		
		for (long m = 1; m*(m + 1)*(2*m + 1) <= 6*x; m++) {
			if (6*x % (m*(m + 1)) != 0) continue;
			long n = 6*x / (m*(m + 1));
			n += m - 1;
			if (n % 3 != 0) continue;
			n /= 3;
			r.add(m + " " + n);
			if (m != n) {
				cnt += 2;
				res.add(n + " " + m);
			}
			else cnt++;
		}
		for (int i = 0; i < r.size(); i++) out.write(r.get(i) + "\n");
		for (int i = res.size() - 1; i >= 0; i--) out.write(res.get(i) + "\n");
		System.out.println(cnt);
		out.flush();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new SpongebobAndSquares().solve();
	}
}