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Problem H
Hill Number
A Hill Number is a positive integer, the digits of which possibly rise and then possibly fall, but never fall and then rise. For example:
12223 is a hill number.
33322111 is a hill number.
1232321 is not a hill number.
Given a positive integer, if it is a hill number, print the number of positive hill numbers less than or equal to it. If it is not a hill number, print -1.
Input
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will consist of a single integer $n$ ($1 \le n \le 10^{18}$).
Output
Output a single line with a single integer. If the input is a hill number, then output the number of hill numbers less than or equal to it. If the input is not a hill number, then output -1.
| Sample Input 1 | Sample Output 1 |
|---|---|
10 |
10 |
| Sample Input 2 | Sample Output 2 |
|---|---|
55 |
55 |
| Sample Input 3 | Sample Output 3 |
|---|---|
101 |
-1 |
| Sample Input 4 | Sample Output 4 |
|---|---|
1234321 |
94708 |
| Sample Input 5 | Sample Output 5 |
|---|---|
1000 |
715 |
