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Points:
100

Time limit:
1.0s

Memory limit:
256M

Author:

Problem types

Allowed languages

C, C++, Java 11, ~~JAVA 8~~, Python, ~~ZIG~~

A googol written out in decimal has 101 digits. A googolplex has one plus a googol digits. That’s a lot of digits! Given any number , define a sequence using the following recurrence:

the number of digits in the decimal representation of

Your task is to determine the smallest positive such that .

#### Input

Input consists of several lines. Each line contains a value of . Every value of is non-negative and has no more than one million digits. The last line of input contains the word `END`

.

#### Output

For each value of given in the input, output one line containing the smallest positive such that .

#### Sample Input

```
42
END
```

#### Sample Output

`3`

## Comments