#P1662. Circle Counting Reversal
Circle Counting Reversal
Circle Counting Reversal
There are 1337 people standing in a circle. They are numbered from 1 to 1337 in clockwise order. Starting from person 1, a number is announced sequentially as 1, 2, 3, ... with the initial direction proceeding clockwise (i.e. increasing order). However, whenever the current number is either a multiple of 7 or contains the digit 7, the direction of counting reverses immediately.
For example, the first 20 numbers and the corresponding person who announces the number are shown in the table below:
| Number X | Person Number |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 6 |
| 9 | 5 |
| 10 | 4 |
| 11 | 3 |
| 12 | 2 |
| 13 | 1 |
| 14 | 1337 |
| 15 | 1 |
| 16 | 2 |
| 17 | 3 |
| 18 | 2 |
| 19 | 1 |
| 20 | 1337 |
Your task is: given a number X, determine which person (their number) will announce the number X.
Note: When moving in the circle, if the person number goes beyond 1337 it wraps around to 1, and if it falls below 1 it wraps around to 1337.
The reversal condition can be stated in LaTeX as follows:
\(\text{Reverse direction if } (X \bmod 7 = 0) \text{ or } (\text{'7' is a digit in } X)\)
inputFormat
The input consists of a single integer X (1 \leq X \leq 10^9), which indicates the count number for which you need to find the person that announces it.
outputFormat
Output a single integer representing the person number who announces the number X.
sample
11