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:
from collections import Counter
def mp():  return map(int,input().split())
def lt():  return list(map(int,input().split()))
def pt(x):  print(x)
def ip():  return input()
def it():  return int(input())
def sl(x):  return [t for t in x]
def spl(x): return x.split()
def aj(liste, item): liste.append(item)
def bin(x):  return "{0:b}".format(x)
def listring(l): return ' '.join([str(x) for x in l])
def printlist(l): print(' '.join([str(x) for x in l]))

n = it()
L = []
R = []
for i in range(1,int((3*n)**(1/3))+1):
    if 6*n % (i*(i+1)) == 0:
        if ((6*n) // (i*(i+1)) + i - 1) % 3 == 0:
            t = ((6*n) // (i*(i+1)) + i - 1) // 3
            L.append([i,t])
            if i < t:
                R.insert(0,[t,i])
result = L + R
print(len(result))
for i in result:
    printlist(i)