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:
n = int(input())
i = 0
s = 0
t = 0
x = 0
f = 0
res1 = []
res2 = []
while n >= 0:
	i = i + 1
	n = n - i * i
	if ( n < 0 ):
		break	
	t = t + i
	m =  n  //  t 
	if  ( m * t !=  n  ):
		continue
	else: 		
		res1.append(  i  )	
		res2.append(  m + i  )	
		x = x + 1
		if m == 0:
			f = 1

print ( str(int(2 * x - f)) )
for i in range(x):
	print( str(int(res1[i])) + " " + str(int(res2[i])))
res1.reverse()
res2.reverse()
for i in range(x):
	if ( res1[i] != res2[i] ):
		print( str(int(res2[i])) + " " + str(int(res1[i])))