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:
s = int(input())
"""
nm + (n-1)(m-1) + ...
nm + nm -(n+m) + 1
6x
= 6mn*n - 3*(n-1)n(n+m) + (n-1)*n*(2n-1)
6x - n*(n+1)*(2n+1)+3*(n-1)n*n = (6n*n - 3*(n-1)*n)*m
"""
a, b = [], []
for n in range(1,1450000):
    u = 6*s - n*(n-1)*(n+n-1)+3*(n-1)*n*n
    v = 6*n*n - 3*(n-1)*n
    if u % v == 0:
        u //= v
        if n <= u:
            a += [(n, u)]
            if n < u:
                b += [(u, n)]
        else:
            break
print(len(a)+len(b))
for e in a:
    print(*e)
for e in reversed(b):
    print(*e)