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.

<image>

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:
x = int(input()) * 6
n, equ, ans = 0, False, []
while True:
	n += 1
	if n * (n + 1) * (2 * n - 1) > x:
		break
	if x % n != 0:
		continue
	if x % (n + 1) != 0:
		continue
	m = x // n // (n + 1) + n - 1
	if m % 3 != 0:
		continue
	m = m // 3
	if n <= m:
		ans.append([n, m])
		if n == m:
			equ = True

print(len(ans) * 2 - equ)
for p in ans:
	print("%d %d" % (p[0], p[1]))
if equ:
	ans.pop()
ans.reverse()
for p in ans:
	p.reverse();
	print("%d %d" % (p[0], p[1]))