| You are writing a new revolutionary archiver. The archive is essentially a | |
| pair of non-decreasing sequences of integers of equal length **K**: | |
| **0≤x1≤...≤xk** and **0≤y1≤...≤yk**. | |
| The decompression algorithm proceeds as follows: | |
| 1. Sequence **(0,0), (x1,y1), ... (xk,yk), (xk, 0), (0, 0)** defines a polygon **P** | |
| 2. Starting from the point **(0,0)**, increase either **x** or **y** coordinate by 1 without moving outside of **P**. If both moves are available, you should increase y. After each step write **0** to output if incremented **x** or **1** otherwise. | |
| 3. Repeat step 2 until you end up in point **(xk,yk)**. | |
| Example: decompression of sequence **(3,4), (7,6), (7,8)** will produce string | |
| **010101100100111**. | |
| Your task is to write a compression rate calculator, that is given binary | |
| string s find the smallest value of **K** for which there exists archive that | |
| decompresses to s. | |
| ## Input | |
| The first line contains a single integer **T**, **T** ≤ 20. **T** test cases | |
| follow, where each test case consists of one binary string with length **≤ | |
| 1,000,000**. | |
| ## Output | |
| Output a single line containing the smallest possible **K**. | |