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.

<image>

Solution (in PYTHON3):

Solution:
def main():
	x = int(input())
	l = squares(x)
	last = l[len(l) - 1]
	if last[0] != last[1]:
		print(2 * len(l))
	else:
		print(2 * len(l) - 1)
	for pair in l:
		print(pair[0], pair[1])
	if last[0] != last[1]:
		for pair in l[::-1]:
			print(pair[1], pair[0])
	else:
		revL = l[::-1]
		for pair in revL[1:]:
			print(pair[1], pair[0])

def squares(x):
	if x == 1:
		return [(1, 1)]
	result = []
	cubeRoot = int((6 * x)**(1/3)) 
	n = 1
	while n <= cubeRoot:
		#m = (y / (n * (n + 1)) + n - 1) / 3
		y = 6 * x
		temp = n * (n + 1)
		if y % temp == 0:
			y //= temp
			y += n - 1
			if y % 3 == 0:
				m = y // 3
				if m >= n:
					result += [(n, m)]
		n += 1
	return result

#main()
main()