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:
import itertools
import math

x = int(input())
kmax = math.floor((3*x) ** (1/3))
ans = []
for i in range(1, kmax+1):
    if 6*x % (i*(i+1)) == 0:
        s = 6*x // (i*(i+1)) + i - 1
        if s % 3 == 0:
            ans.append((i,s//3))


res = 2*len(ans) - 1 if ans[-1][0] == ans[-1][1] else 2*len(ans)
print(res)
for pair in ans[:-1]:
    print(pair[0], pair[1])

if res%2 == 0: print(ans[-1][0], ans[-1][1])

for pair in reversed(ans):
    print(pair[1], pair[0])