Problem K
Persistent Numbers
The multiplicative persistence of a number is defined by Neil Sloane (Neil J.A. Sloane in The Persistence of a Number published in Journal of Recreational Mathematics 6, 1973, pp. 97-98., 1973) as the number of steps to reach a one-digit number when repeatedly multiplying the digits. For example:
\[ 697 \rightarrow 378 \rightarrow 168 \rightarrow 48 \rightarrow 32 \rightarrow 6 \]That is, the persistence of $697$ is $5$. The persistence of a single digit number is $0$. At the time of this writing it is known that there are numbers with the persistence of $11$. It is not known whether there are numbers with the persistence of $12$, but it is known that if they exist then the smallest of them would have more than $3000$ digits.
The problem that you are to solve here is: what is the smallest number such that the first step of computing its persistence results in the given number?
Input
The input consists of multiple test cases. Each line contains a test case, which consists of a decimal number with up to $1\, 000$ digits. The input ends with a line containing -1.
There will be at most $50$ test cases in a single input file.
Output
For each testcase, output a single line containing one integer number satisfying the condition stated above. If no such number exists, output “There is no such number”.
| Sample Input 1 | Sample Output 1 |
|---|---|
0 1 4 7 18 49 51 768 -1 |
10 11 14 17 29 77 There is no such number. 2688 |
