Dimash learned that Mansur wrote something very unpleasant about him to a friend, so he decided to find out his password at all costs and discover what exactly he wrote.

Believing in the strength of his password, Mansur stated that his password — is a binary string of length $$$n$$$. He is also ready to answer Dimash's questions of the following type:

Dimash says a binary string $$$t$$$, and Mansur replies whether it is true that $$$t$$$ is a substring of his password.

Help Dimash find out the password in no more than $$$2n$$$ operations; otherwise, Mansur will understand the trick and stop communicating with him.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.
Example Input 0:
4
3

0

0

1

4

4

2

Example Output 0:
? 00

? 000

? 010

! 010

! 1100

! 0110

! 10

Notes:
In the first example, the string $$$010$$$ is given. Therefore, the answers to the queries are as follows:

"? 00" $$$00$$$ is not a substring of $$$010$$$, so the answer is $$$0$$$.

"? 000" $$$000$$$ is not a substring, so the answer is $$$0$$$.

"? 010" $$$010$$$ is a substring, so the answer is $$$1$$$.

In the second example, the string is $$$1100$$$, in the third $$$0110$$$, and in the fourth $$$10$$$.

Example input:
4
3

0

0

1

4

4

2


Example output:
? 00

? 000

? 010

! 010

! 1100

! 0110

! 10