This is an interactive problem.

KUPC-kun wrote a program that solves the following problem.

You are given a tree $T = (V, E)$ with $N$ vertices. For a sequence $\{a_1, \dots, a_k\}$ of vertices of $T$ of length $k$, define its score as follows. - Let $d(u, v)$ be the number of edges on the path between vertices $u$ and $v$ in $T$. Then the score is $\prod_{i=1}^k d(a_i, a_{(i \bmod k)+1})$.

A subset $S$ of $V$ is given. For each $1 \le k \le N$, find the following value $q_k$. - The sum of the scores over all vertex sequences $\{a_1, \dots, a_k\}$ of length $k$ whose elements belong to $S$, taken modulo $2^{61} - 1$.

KUPC-kun secretly keeps the information of the tree $T$ in advance, and continues using $T$ as the tree given to the program.

You are trying to recover the information of the leaves using the above program. Letting the number of vertices of the tree be $N$, you may ask the following question at most $N$ times.

• Choose a subset $S$ of $V$ and ask for the output of the program.

Assuming that KUPC-kun's program is correct, identify all leaves contained in the tree $T$ from the information obtained through the questions.

The judge is not adaptive, and the tree $T$ is fixed before the interaction begins.

Interaction Protocol

First, $N$ is given from standard input. ($2 \le N \le 50$)

For each question, output to standard output in the following format.

? s1s2...sN

Here, $s_1s_2\cdots s_N$ is a string of length $N$ representing the subset $S$, where $s_i = 1$ if $i \in S$, and $s_i = 0$ if $i \notin S$.

In response, the following is given from standard input.

q1 q2 ... qN

Once you have identified all leaves, output your answer in the following format.

! t1t2...tN

Here, $t_1t_2\cdots t_N$ is a string of length $N$, where $t_i = 1$ if $i$ is a leaf, and $t_i = 0$ if it is not a leaf.

After this output, terminate your program immediately.

Whenever you output something, append a newline at the end and flush standard output.

Example

Sample Input 1

5

0 8 0 32 0

0 44 108 968 3960

0 0 0 0 0

0 76 348 3336 22200

Sample Output 1

? 00101

? 11001

? 10000

? 11111

! 11001

Note

For the first example, the edge set of the tree secretly held by the judge is $(1, 3), (2, 3), (3, 4), (4, 5)$.

In the first question, $S = \{3, 5\}$.

Note that $d(3, 3) = 0, d(3, 5) = d(5, 3) = 2, d(5, 5) = 0$.

For example, there are the following $4$ vertex sequences $a$ of length $2$ whose elements belong to $S$.

• If $a = (3, 3)$, then the score of this sequence is $d(3, 3) \times d(3, 3) = 0 \times 0 = 0$.
• If $a = (3, 5)$, then the score of this sequence is $d(3, 5) \times d(5, 3) = 2 \times 2 = 4$.
• If $a = (5, 3)$, then the score of this sequence is $d(5, 3) \times d(3, 5) = 2 \times 2 = 4$.
• If $a = (5, 5)$, then the score of this sequence is $d(5, 5) \times d(5, 5) = 0 \times 0 = 0$.

The judge responds with $8$ for $q_2$, which is the remainder when $0 + 4 + 4 + 0$ is divided by $2^{61} - 1$.

By computing similarly for the other sequence lengths, we obtain the judge's response 0 8 0 32 0.

The leaves of this tree are vertices $1, 2, 5$, and outputting ! 11001 correctly completes the identification of the leaves.