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≤...≤x_k and 0≤y₁≤...≤y_k.

The decompression algorithm proceeds as follows:

1. Sequence (0,0), (x₁,y₁), ... (x_k,y_k), (x_k, 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 (x_k,y_k).

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.