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:
x = int(input())

def solve(x):
    count = 0
    lst = []
    x6 = x * 6
    for n in range(1, x + 1):
        t, r = divmod(x6, n*(n+1))
        if t < 2*n + 1:
            break
        if r:
            continue
        m, r = divmod(t + n - 1, 3)
        if r:
            continue
        count += 2
        lst.append((n, m))
    nn, mm = lst[-1]
    if nn == mm:
        count -= 1
    print(count)
    for n, m in lst:
        print(n, m)
    if nn != mm:
        print(mm, nn)
    lst.reverse()
    for n, m in lst[1:]:
        print(m, n)

solve(x)