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.PrintWriter;
import java.math.BigInteger;
import java.util.Scanner;
import java.util.TreeSet;

public class D {
	// 1000000000000000000
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		PrintWriter out =new PrintWriter(System.out);
		long x = scan.nextLong();
		BigInteger bx = BigInteger.valueOf(x);
		long sqrt = (long) Math.sqrt(x);
		long height = 1;
		TreeSet<Pair> ts = new TreeSet<>();
		while (height <= x) {
			BigInteger bh = BigInteger.valueOf(height);
			BigInteger num = bh.multiply(bh).multiply(bh).subtract(bh).add(BigInteger.valueOf(6).multiply(bx));
			BigInteger den = BigInteger.valueOf(3).multiply(bh).multiply(bh.add(BigInteger.ONE));
			BigInteger bi = num.divide(den);
			long rough;
			try {
				rough = bi.longValueExact();
			} catch(ArithmeticException e) {
				break;
			}
			if(rough+1 < height)
				break;
			if(num.mod(den).equals(BigInteger.ZERO)) {
				ts.add(new Pair(height, rough));
				ts.add(new Pair(rough, height));
			}
			height++;
		}
		out.println(ts.size());
		for (Pair p : ts) {
			out.println(p);
		}
		out.close();
	}
	static class Pair implements Comparable<Pair> {
		long w, h;
		public Pair(long w, long h) {
			this.w = w;
			this.h = h;
		}
		@Override
		public int compareTo(Pair o) {
			if(w == o.w)
				return Long.compare(h, o.h);
			return Long.compare(w, o.w);
		}
		@Override
		public String toString() {
			return w + " " + h;
		}
		
	}
}