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 PYTHON3):

Solution:
#from time import time

def solve( x ):

    res = [(1,x)]
    if x != 1:
        res.append( (x,1) )

    index , a , b = 1 , 1 , 0
    while True:
        b += a
        index += 1
        a += index

        if a*index-b > x:
            break

        if ( x + b ) % a == 0:
            m = ( x + b )// a
            res.append( ( index , m ) )
            if index != m:
                res.append( ( m , index ) )

    res.sort()
    print( len(res) )
    for ares in res:
        print( ares[0] , ares[1] )

if __name__ == "__main__":

    #t1 = time()
    x = int( input() )
    solve( x )
    #t2 = time()
    #print( "time :" , t2-t1 , "s" )