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.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Random;
import java.util.Scanner;

public class CFProblemD {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner input = new Scanner(System.in);
		long inputLong = (long) input.nextLong();
		long specialMagicSum = 0;
		ArrayList<Long> results = new ArrayList<Long>();
		ArrayList<Long> results2 = new ArrayList<Long>();
		BigInteger largeNumber = new BigInteger("" + inputLong);
		for (long a = 1; a < 1500000; a++) {
			largeNumber=largeNumber.add(new BigInteger("" + (a * (a - 1) / 2)));
			BigInteger temp = new BigInteger("" + (a * (a + 1) / 2));
			if (largeNumber.mod(temp).equals(BigInteger.ZERO)) {
				if (a <= (largeNumber.divide(temp)).longValue()) {
					results.add(a);
					results2.add(largeNumber.divide(temp).longValue());
				}
				
			}
			if (a > (largeNumber.divide(temp)).longValue()) {
				break;
			}
		}
		boolean duplicate =  true;
		if(results.size() > 0){
		   duplicate = (results2.get(results.size()-1).equals(results.get(results.size()-1)));
		}
		System.out.println(results.size() * 2 - ((duplicate)?1:0));
		for (int a = 0; a < results.size() - ((duplicate)?1:0); a++) {
			System.out.println(results.get(a) + " " + results2.get(a));
		}
		for (int a = results.size()-1; a >= 0; a--) {
			System.out.println(results2.get(a) + " " + results.get(a));
		}
	}
}