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.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main
{

    void solve() throws Exception
    {
        long x = nextLong();
        ArrayList<long[]> ans = new ArrayList<>();
        long sqrsum = 0;
        long nsum = 0;
        for( long n = 1;; n++ )
        {
            sqrsum += n * n;
            nsum += n;
            long ynsum = x - sqrsum;
            if( ynsum < 0 ) break;
            if( ynsum % nsum == 0 )
            {
                ans.add( new long[] { n, n + ynsum / nsum } );
            }
        }
        for( int i = ans.size() - 1; i >= 0; i-- )
        {
            long[] q = ans.get( i );
            if( q[ 0 ] == q[ 1 ] ) continue;
            ans.add( new long[] { q[ 1 ], q[ 0 ] } );
        }
        out.println( ans.size() );
        for( long[] q : ans )
        {
            out.println( q[ 0 ] + " " + q[ 1 ] );
        }
    }


    public static void main( String[] args )
    {
        new Main().run();
    }

    public void run()
    {
        try
        {
            in = new BufferedReader( new InputStreamReader( System.in ) );
            out = new PrintWriter( System.out );
            solve();
        }
        catch( Exception e )
        {
            e.printStackTrace();
            System.exit( 1 );
        }
        finally
        {
            out.close();
        }
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st;

    String nextToken() throws IOException
    {
        while( st == null || !st.hasMoreTokens() ) st = new StringTokenizer( in.readLine() );
        return st.nextToken();
    }

    int nextInt() throws IOException
    {
        return Integer.parseInt( nextToken() );
    }

    long nextLong() throws IOException
    {
        return Long.parseLong( nextToken() );
    }

}