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 PYTHON):

Solution:
def func(x):
    t = int((3*x) ** (1.0/3))
    ans = []
    for m in range(1,t+1):
        top = (m**3 - m + 6*x)
        bottom = 3*m*(m+1)
        if top % bottom == 0:
            ans.append([ m , top / bottom])

    return ans

x = input()
ans = func(x)

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