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 PYTHON):

Solution:
from math import *
from fractions import *

l = []

def solve():
	x = int(raw_input())
	
	n = 1
	while True:
		t1 = (n*n) - ((n*(n-1))/2)
		t2 = ((n-1)*n*(2*n-1))/6
		t2 -= (n*n*(n-1))/2
		
		if x-t2 < n*t1:
			break
		
		m = (x-t2)/t1
		if m*t1 == x-t2:
			l.append((n,m))
			if n != m:
				l.append((m,n))
		n += 1
	l.sort()
	print len(l)
	
	for pair in l:
		print pair[0], pair[1]
	
	return

solve()