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 calcm(n, x):
    x *= 6
    m = (n * n * n - n + x) / (3 * n * n + 3 * n)
    if (n * n * n - n + x) % (3 * n * n + 3 * n) == 0:
        return [True, m]
    return [False, m]

x = input()
xroot = x ** 0.5
xroot = int(xroot)+1
xroot = min(xroot, 2000002)
rs = []
rs2 = []
for i in xrange(1, xroot + 1):
    r = calcm(i, x)
    if r[0]:
        if r[1] < i:
            break
        cur=str(i)+" "+str(r[1])
        rs.append(cur)
        if i <> r[1]:
            cur=str(r[1])+" "+str(i)
            rs2.append(cur)

print len(rs)+len(rs2)
print '\n'.join(rs)
rs2.reverse()
print '\n'.join(rs2)