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:
import sys, traceback

def test():
    text = sys.stdin.readlines()
    n = long(text[0])

    factors = []

    for i in xrange(1, 10**9):
        # compute rectangular pyramid components
        base = (2*i*i*i + 3*i*i + i)/6
        if base > n: # passed the pyramid root
            return factors, False
        wing = i*(i+1)/2
        q, r = divmod(n - base, wing)
        if r == 0:
            factors.append((i,i+q))
            if q == 0: # reached the pyramid root
                return factors, True

    return factors

def run():
    ans, square = test()
    if not square:
        print len(ans)*2
        for x,y in ans:
            print x,y
        for x,y in ans[::-1]:
            print y,x
    else:
        print len(ans)*2-1
        for x,y in ans[:len(ans)-1]:
            print x,y
        for x,y in ans[::-1]:
            print y,x

if __name__ == "__main__":
    try:
        run()
    except Exception, err:
        print err
        traceback.print_exc(file=sys.stdout)