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:
x=int(input())
a=1
ans=[]
t=set()
while a*a*a<=3*x:
    if a in t:
        break
    if (((a*a*a-a)//3)+2*x)%(a*a+a)==0:
        b=(((a*a*a-a)//3)+2*x)//(a*a+a)
        ans.append([a,b])
        if a!=b:
            ans.append([b,a])
        t.add(a)
        t.add(b)
    a+=1
print(len(ans))
ans=sorted(ans, key=lambda student: student[0]) 
for i in ans:
    c=[]
    c.append(str(i[0]))
    c.append(str(i[1]))
    print(' '.join(c))