AT_abc415_c [ABC415C] Mixture

There are $ N $ types of chemicals $ 1,2,\dots,N $ . Your goal is to create a state where all of them are mixed. You are given a string $ S $ of length $ 2^N-1 $ consisting of `0` and `1`, which represents the following information: - First, define state $ i $ ( $ 1 \le i \le 2^N-1 $ ) where one or more types of chemicals are mixed as follows: - When the $ k $ -th digit ( $ 1 \le k \le N $ ) from the bottom in the binary representation of $ i $ is $ 1 $ , and only then, chemical $ k $ is included. - For example, $ 13 $ in binary is $ 1101_{(2)} $ , so state $ 13 $ represents a state where chemicals $ 1,3,4 $ are mixed. - When the $ i $ -th character of $ S $ is `0`, state $ i $ is **safe**. - When the $ i $ -th character of $ S $ is `1`, state $ i $ is **dangerous**. You mix chemicals using the following operation: - First, prepare an empty bottle. - Next, repeat the following: - Choose one type of chemical that has not yet been poured into the bottle and pour it into the bottle. - At this time, the chemicals mixed in the bottle must not be in a dangerous state. Determine whether this operation can create a state where all chemicals are mixed. You are given $ T $ test cases; solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ $ \mathrm{case}_i $ represents the $ i $ -th test case. Each test case is given in the following format: > $ N $ $ S $

Output $ T $ lines. The $ i $ -th line should contain the answer for the $ i $ -th test case. For each test case, if it is possible to create a state where all chemicals are mixed, print `Yes`; otherwise, print `No`.

### Sample Explanation 1 This input contains five test cases. The $ 1 $ st case is as follows: - There are three types of chemicals. - Only state $ 3 $ where chemicals $ 1,2 $ are mixed is dangerous, and the other states are safe. - For example, you can create a state where all chemicals are mixed with the following procedure: - First, pour chemical $ 2 $ into the bottle. Only chemical $ 2 $ is mixed in the bottle, which is state $ 2 $ , so it is safe. - Next, pour chemical $ 3 $ into the bottle. Chemicals $ 2,3 $ are mixed in the bottle, which is state $ 6 $ , so it is safe. - Finally, pour chemical $ 1 $ into the bottle. Chemicals $ 1,2,3 $ are mixed in the bottle, which is state $ 7 $ , so it is safe. The $ 2 $ nd case is as follows: - There are three types of chemicals. - State $ 3 $ where chemicals $ 1,2 $ are mixed, state $ 5 $ where chemicals $ 1,3 $ are mixed, and state $ 6 $ where chemicals $ 2,3 $ are mixed are dangerous, and the other states are safe. - For this case, it is impossible to create a state where all chemicals are mixed. The $ 3 $ rd case is as follows: - There is one type of chemical. - Since state $ 1 $ where only chemical $ 1 $ is mixed is dangerous, it is impossible to create a state where all chemicals are mixed. ### Constraints - $ T $ is an integer between $ 1 $ and $ 40000 $ , inclusive. - $ N $ is an integer between $ 1 $ and $ 18 $ , inclusive. - $ S $ is a string of length $ 2^N-1 $ consisting of `0` and `1`. - The sum of $ |S| = 2^N-1 $ in each input does not exceed $ 5 \times 10^5 $ .