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.*;
import java.io.*;

public class D {
	FastScanner in;
	PrintWriter out;

	class Answer {
		long a, b;

		public Answer(long a, long b) {
			super();
			this.a = a;
			this.b = b;
		}
	}

	public void solve() throws IOException {
		long x = in.nextLong();
		ArrayList<Answer> ans = new ArrayList<>();
		long sum = 0;
		for (long k = 1;; k++) {
			sum += k * k;
			long y = x - sum;
			if (y < 0) {
				break;
			}
			y *= 2;
			if (y % k == 0 && y % (k + 1) == 0) {
				y /= k;
				y /= (k + 1);
				long a = k, b = y + k;
				if (a <= b) {
					ans.add(new Answer(a, b));
					if (a < b) {
						ans.add(new Answer(b, a));
					}
				}
			}
		}
		Collections.sort(ans, new Comparator<Answer>() {
			@Override
			public int compare(Answer o1, Answer o2) {
				if (o1.a != o2.a) {
					return Long.compare(o1.a, o2.a);
				}
				return Long.compare(o1.b, o2.b);
			}
		});
		out.println(ans.size());
		for (Answer a : ans) {
			out.println(a.a + " " + a.b);
		}
	}

	public void run() {
		try {
			in = new FastScanner();
			out = new PrintWriter(System.out);

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}

	public static void main(String[] arg) {
		new D().run();
	}
}