Problem D
Pinni Frændi
Languages
en
is
Hannes was ordering a pizza, but had forgotten his PIN, as per usual. Luckily he has it saved in the contact Pinni Frændi on his phone. While he was still looking at that contact he got the confirmation number from Panucci’s Pizza. Surprisingly enough his PIN number and the confirmation code were the same! What are the chances? The code is chosen uniformly at random among all possible codes of the right length. The only valid characters in the code are the digits $0$ to $9$.
Input
The first and only line of input contains a positive integer $n$, the number of digits in the PIN and the confirmation code.
Output
Output the probability that the code and PIN are the same. This should be printed as an exact decimal. Extra zeroes should not be printed.
Scoring
|
Group |
Points |
Constraints |
|
1 |
50 |
$1 \leq n \leq 4$ |
|
2 |
50 |
$5 \leq n \leq 1\, 000$ |
| Sample Input 1 | Sample Output 1 |
|---|---|
4 |
0.0001 |
| Sample Input 2 | Sample Output 2 |
|---|---|
8 |
0.00000001 |
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