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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class D {
	long x;
	void readInput() throws NumberFormatException, IOException{
		//BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Scanner sc = new Scanner(System.in);
		x = sc.nextLong();
	}
	class Pair implements Comparable<Pair>{
		long i,x;
		Pair(long i, long x){
			this.i=i; this.x=x;
		}		
		public String toString(){
			return x+" "+i;
		}
		public int hashCode(){
			return (int)(i^ x);
		}
		public boolean equals(Object arg0){
			Pair p = (Pair)arg0;
			return (x == p.x && i == p.i);
		}
		@Override
		public int compareTo(Pair o) {
			if (x==o.x)
				return Long.compare(i, o.i);
			return Long.compare(x, o.x);
		}
	}
	void solve(){
		long m1, m2, m;		
		ArrayList<Pair>  pp = new ArrayList<Pair>();
		for(long n=1; n<=x; n++){
			m1 = x - n*(n+1)*(2*n+1)/6;			
			m2 = n*(n+1)/2;			
			if (m1<0)
				break; //breaks at x^1/3
			if (m1 % m2 == 0){
				m = n+m1/m2;				
				pp.add(new Pair(n, m));
				if (n!=m)
					pp.add(new Pair(m, n));
			}				
		}
		Collections.sort(pp);
		System.out.println(pp.size());
		for(Pair p:pp)
			System.out.println(p);
	}

	public static void main(String[] args) throws NumberFormatException, IOException {
		D a = new D();
		a.readInput();
		a.solve();
	}

}