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 squares(sh, lo):
    return sh * (sh + 1) * (3 * lo - sh + 1) // 6 

MAX_A = 10**18

def find_max(condition, minv, maxv):
    if minv + 1 >= maxv:
        return max([x for x in (minv, maxv) if condition(x)])
    avg = (minv + maxv) // 2 

    if condition(avg):
        boundaries = [avg, maxv]
    else:
        boundaries = [minv, avg]
    return find_max(condition, boundaries[0], boundaries[1])

def solve(n):
    part = []
    sh = 1 
    while True:
        if ((6 * n) % (sh * (sh + 1)) == 0) or (sh % 100 == 0):
            lo = find_max(lambda x: squares(sh, x) <= n, 0, MAX_A)
            if lo >= sh and squares(sh, lo) == n:
                part.append((sh, lo))
            if lo < sh:
                return sorted(list(set(part).union(set((j, i) for (i, j) in part))))
        sh += 1 
        
n = int(input())
result = solve(n)
print(len(result))
for r in result:
    print("%s %s" % r)