JUMP Interactive Problem

This is an interactive problem called JUMP based on the toy interactive problem ONEMAX. You are given an even integer \(n\) that denotes the length of a hidden bit-string \(S\). The only allowed operation is to query the system with a bit-string \(Q\) of length \(n\). The system returns a value according to the following rule:

[ \text{JUMP}(Q)= \begin{cases} \text{ONEMAX}(Q) & \text{if } \text{ONEMAX}(Q)=n \text{ or } \text{ONEMAX}(Q)=\frac{n}{2}; \ 0 & \text{otherwise,} \end{cases} ]

Here, \(\text{ONEMAX}(Q)\) is the number of positions where the query \(Q\) matches the hidden string \(S\). In other words:

[ \text{ONEMAX}(Q)=\sum_{i=1}^{n}[Q_i=S_i]. ]

Your objective is to eventually make a query \(Q\) such that \(Q=S\). When you submit a query where \(Q=S\), the system returns \(n\) and terminates the interaction. Note that you are allowed to make at most \(n+500\) queries.

Interaction protocol:

• The system first outputs the integer \(n\) (the length of the bit-string).
• Your solution then makes queries by printing a bit-string \(Q\) of length \(n\).
• For each query, the system responds with either \(n\), \(\frac{n}{2}\), or \(0\) according to the rule above.
• If your query equals the hidden string \(S\), the interaction ends with the system outputting \(n\).

For the purpose of testing in a non-interactive environment, the input will consist of two lines: the first line contains \(n\) and the second line contains the hidden bit-string \(S\). Your program should output the hidden bit-string \(S\).

inputFormat

The input consists of two lines:

1. The first line contains an even integer \(n\) ( \(2 \leq n \leq 10^4\) for instance).
2. The second line contains a hidden bit-string \(S\) of length \(n\) (each character is either '0' or '1').

outputFormat

Output a single line containing the hidden bit-string \(S\). Your output should exactly match the hidden string.

sample

4
0101

0101