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.

<image>

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:
"""
Codeforces Round #332 (Div. 2)

Problem 599 D. Spongebob and Squares

@author yamaton
@date 2015-11-20
"""

import itertools as it
import functools
import operator
import collections
import math
import sys


def solve(x):
    def find_p(n):
        return (6 * x // (n * (n + 1)) - 2 * n - 1) // 3
    def f(n, p):
        return n * (n + 1) * (2 * n + 3 * p + 1) - 6 * x

    result = []
    for n in it.count(1):
        p = find_p(n)
        if p < 0:
            break
        if f(n, p) == 0:
            result.append((n, n + p))
            if p > 0:
                result.append((n + p, n))
    result.sort()
    return result


# def p(*args, **kwargs):
#     return print(*args, file=sys.stderr, **kwargs)


def main():
    x = int(input())
    results = solve(x)
    print(len(results))
    for res in results:
        print(*res)



if __name__ == '__main__':
    main()