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())
i = 1
nmList = []
while True:
    if i * (i + 1) * (2 * i + 1) > 6 * x:
        break
    if (6 * x) % (i * (i+1)) == 0 and ((6 * x) // (i * (i+1)) - (2 * i + 1)) % 3 == 0:
        nmList.append((i,i + ((6 * x) // (i * (i+1)) - (2 * i + 1)) // 3))
    i += 1
number = 0
for elem in nmList:
    if elem[0] != elem[1]:
        number += 2
    else:
        number += 1
print(number)
for elem in nmList:
    print(str(elem[0]) + ' ' + str(elem[1]))
for i in range(len(nmList) - 1, -1, -1):
    elem = nmList[i]
    if elem[0] == elem[1]:
        continue
    print(str(elem[1]) + ' ' + str(elem[0]))