p02694 AtCoder Beginner Contest 165 - 1%
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.

The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)

Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?

Constraints

* 101 \le X \le 10^{18}
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


X


Output

Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.

Examples

Input

103


Output

3


Input

1000000000000000000


Output

3760


Input

1333333333


Output

1706
```python
x=int(input())

a=100
b=0
while a<x:
  b=b+1
  a=(a*1.01)//1
  
print(b)
```