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:
x = int(input())
if x == 1:
	a = [(1, 1)]
a = []
cor = int((6 * x)** (1/3)) 
n = 1
while n <= cor:
	y = 6 * x
	tec = n * (n + 1)
	if y % tec == 0:
		y //= tec
		y += n - 1
		if y % 3 == 0:
			m = y // 3
			if m >= n:
				a += [(n, m)]
	n += 1
p = a[len(a) - 1]
if p[0] != p[1]:
	print(2 * len(a))
else:
	print(2 * len(a) - 1)
for i in a:
	print(i[0], i[1])
if p[0] != p[1]:
	for i in a[::-1]:
		print(i[1], i[0])
else:
	for i in a[::-1][1:]:
		print(i[1], i[0])