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.*;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

/**
 * Created by peacefrog on 11/23/15.
 * Time : 12:53 PM
 */

public class CF599D {
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	PrintWriter out;
	long timeBegin, timeEnd;

	public void runIO() throws IOException {
		timeBegin = System.currentTimeMillis();

		InputStream inputStream;
		OutputStream outputStream;


		if (ONLINE_JUDGE) {
			inputStream = System.in;
			Reader.init(inputStream);
			outputStream = System.out;

			out = new PrintWriter(outputStream);

		} else {
			inputStream = new FileInputStream("/home/peacefrog/Dropbox/IdeaProjects/Problem Solving/input");
			Reader.init(inputStream);
			out = new PrintWriter("output.txt");
		}

		solve();

		out.flush();
		out.close();
		timeEnd = System.currentTimeMillis();

		System.err.println("Time = " + (timeEnd - timeBegin));

	}

	/*
	 * Start Solution Here
	 */

	class pair implements Comparable<pair>{
		long  a , b ;

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

		@Override
		public int compareTo(pair o) {
			int ret = Long.compare(  a , o.a);
			if(ret == 0)
			{
				return Long.compare(b , o.b);
			}

			return ret;
		}
	}
	private void solve() throws IOException {
		long n = Reader.nextLong(); //This Variable default in Code Templete
		PriorityQueue<pair> a = new PriorityQueue<>();
		for(long i = 1 ; i <= 1500000 ; i++)
		{
			long res = (6*n) /(i * (i+1)) ;
			if(((6*n) %(i * (i+1))) != 0 ) continue;
			if((res+i-1) % 3 != 0 ) continue;

			res = res + i -1 ;
			res /= 3 ;
			if(i > res)
				break;
			if(res == i)
			{
				a.add(new pair(i , res));
			}
			else {
				a.add(new pair(i , res));
				a.add(new pair(res ,i ));
			}

		}

		System.out.println(a.size());
		while (!a.isEmpty())
		{
			pair p = a.poll();
			System.out.println(p.a + " " + p.b);
		}
	}

	public static void main(String[] args) throws IOException {

		new CF599D().runIO();
	}

	static class Reader {
		static BufferedReader reader;
		static StringTokenizer tokenizer;

		/**
		 * call this method to initialize reader for InputStream
		 */
		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}

		/**
		 * get next word
		 */
		static String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		static String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return "";
		}

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

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

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

		static long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}

			return arr;
		}

		static int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}

			return arr;
		}
	}

}