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:
__author__ = 'MoonBall'

import sys
# sys.stdin = open('data/D.in', 'r')
T = 1

def process():
    ans = []
    N = int(input())
    for i in range(1, N + 1):
        a = N + i * (i - 1) * (i + 1) // 6
        j, mod = divmod(a, i * (i + 1) // 2)
        if i > j: break
        if mod: continue
        ans.append((i, j))
        if i != j: ans.append((j, i))

    ans.sort()
    print(len(ans))
    for i, j in ans: print(i, j)





for _ in range(T):
    process()