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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class R332Div2D {
	static final int MAX=2000000;
	static long[] square=new long[MAX+1];
	public static void main(String[] args) {
		FastScanner in=new FastScanner();
		long x=in.nextLong();
		
		for(int i=1;i<=MAX;i++)
			square[i]=square[i-1]+i*1L*i;
		
		TreeMap<Long,Long> ans=new TreeMap<Long,Long>();
		for(int i=1;i<=MAX;i++){
			long xx=x-square[i-1]+i*1L*i*(i-1)/2;
			long yy=i*1L*i-i*1L*(i-1)/2;
			if(xx>0&&yy>0&&xx%yy==0&&i<=xx/yy){
				ans.put(i+0L,xx/yy);
				ans.put(xx/yy,i+0L);
			}
		}
		
		PrintWriter out=new PrintWriter(System.out);
		out.println(ans.size());
		for(long k:ans.keySet())
			out.println(k+" "+ans.get(k));
		out.flush();
		out.close();
	}

	static class FastScanner{
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(){br=new BufferedReader(new InputStreamReader(System.in));}
		String nextToken(){
			while(st==null||!st.hasMoreElements())
				try{st=new StringTokenizer(br.readLine());}catch(Exception e){}
			return st.nextToken();
		}
		int nextInt(){return Integer.parseInt(nextToken());}
		long nextLong(){return Long.parseLong(nextToken());}
		double nextDouble(){return Double.parseDouble(nextToken());}
	}
}