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.IOException;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.TreeSet;

public class CF_275_d {
	public static int mod=(int)1e9+7;
	
	
	
	public static void main(String[] args)
	{
    	
		FasterScanner s=new FasterScanner();
		PrintWriter out=new PrintWriter(System.out);
		
		long x=s.nextLong();
		int max=(int)(1e5);
		max=max*15;
		ArrayList<Pair> ans=new ArrayList<>();
		for(long m=1;m<=max;m++)
		{
			if((x+((m*m*m-m*m)/2)-(m*(m-1)*(2*m-1)/6))%((m*m+m)/2)==0)
			{
				long n=(x+((m*m*m-m*m)/2)-(m*(m-1)*(2*m-1)/6))/((m*m+m)/2);
				if(m>n)
					break;
				ans.add(new Pair(m, n));
				if(m!=n)
				ans.add(new Pair(n, m));
			}
		}
		
		Collections.sort(ans);
		System.out.println(ans.size());
		for(Pair p:ans)
			System.out.println(p.m+" "+p.n);
		out.close();
	}
	public static  class Pair implements Comparable<Pair>
	{
		long m,n;
		Pair(long m,long n)
		{
			this.m=m;
			this.n=n;
		}
		@Override
		public int compareTo(Pair o) {
			if(m!=o.m)
				return Long.compare(m, o.m);
			return Long.compare(n, o.n);
		}
		
	}

	public static int pow(int x, int n, int mod) {
		int res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (int) (res * p % mod);
			}
		}
		return res;
	}
    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int tmp_curChar;
        private int tmp_numChars;

        public int read() {
            if (tmp_numChars == -1)
                throw new InputMismatchException();
            if (tmp_curChar >= tmp_numChars) {
                tmp_curChar = 0;
                try {
                    tmp_numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (tmp_numChars <= 0)
                    return -1;
            }
            return buf[tmp_curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
           
        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
       
        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}