Contest Duration: - (local time) (100 minutes) Back to Home
B - 1% /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

AtCoder銀行では、毎年預金額の 1 % の利子がつきます(複利、小数点以下切り捨て)。

### 制約

• 101 \le X \le 10^{18}
• 入力はすべて整数

### 入力

X


### 入力例 1

103


### 出力例 1

3

• 1 年後の預金額は 101 円です。
• 2 年後の預金額は 102 円です。
• 3 年後の預金額は 103 円です。

したがって、預金額が初めて 103 円以上になるのは 3 年後です。

### 入力例 2

1000000000000000000


### 出力例 2

3760


### 入力例 3

1333333333


### 出力例 3

1706


Score : 200 points

### Problem Statement

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.

### Sample Input 1

103


### Sample Output 1

3

• The balance after one year is 101 yen.
• The balance after two years is 102 yen.
• The balance after three years is 103 yen.

Thus, it takes three years for the balance to reach 103 yen or above.

### Sample Input 2

1000000000000000000


### Sample Output 2

3760


### Sample Input 3

1333333333


### Sample Output 3

1706