Problem G
The Secret Key
You are a security expert hired to manage the digital access for a massive factory. The factory utilizes $N$ special lockboxes, and each requires a unique key. Each key is a $N$-digit binary string (composed of only $0$s and $1$s).
You are given a list, used_keys, containing all $N$ unique keys currently assigned to the lockboxes. The Chief Security Officer requires you to generate a guaranteed new $N$-digit binary key to secure a new, super secret lockbox. This new key, new_key, must not match any key currently in the used_keys list.
Since the total number of possible $N$-digit binary keys is $2^N$, and you are only given $N$ used keys, a new key is guaranteed to exist. Your task is to construct one such key.
Input
The input consists of $N+1$ lines. The first line contains a single integer, $N$, the number of used keys and the length of each key ($1 \le N \le 100$). The next $N$ lines each contain a unique binary string of length $N$, representing the used_keys.
Output
Output a single line containing the constructed binary string, new_key, of length $N$. Any valid, unique key that is not present in the input list will be accepted.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 001 110 010 |
000 |
| Sample Input 2 | Sample Output 2 |
|---|---|
1 0 |
1 |
| Sample Input 3 | Sample Output 3 |
|---|---|
2 00 11 |
10 |
| Sample Input 4 | Sample Output 4 |
|---|---|
4 0000 1111 0101 1010 |
1011 |
