Binary Word Restoration

A sender transmits a binary word through a tunnel. Initially, each word is composed of 0's and 1's and has a fixed length n (4 ≤ n ≤ 1000). Moreover, every original word has the following property: if you sum up the positions (1-indexed) of all the 1's in the word, the result is either 0 or a multiple of \(n+1\) (i.e. if we denote the sum by \(S\), then \(S \equiv 0 \pmod{n+1}\)).

However, during transmission through the tunnel, exactly one of the following modifications may occur:

1. Any one occurrence of 0 may be changed into a 1 (substitution error).
2. Any one symbol (either 0 or 1) may be deleted (deletion error).
3. A symbol (either 0 or 1) may be inserted at any position (insertion error).
4. No change occurs (i.e. the word remains intact).

Your task is to recover the original word given the received word. Note that the received word may have length n, n-1, or n+1 depending on the operation error that occurred. It is guaranteed that there is a unique original word S of length n (which contains only characters 0 and 1 and satisfies \(\sum_{i=1}^{n} i \cdot [S_i = '1'] \equiv 0 \pmod{n+1}\)) such that the received word can be obtained from S by exactly one of the four operations described above.

Note: In all formulas, positions in a word are numbered from 1 to n. The notation \([S_i = '1']\) equals 1 if the i-th character is 1 and 0 otherwise.

inputFormat

The first line contains an integer n (4 ≤ n ≤ 1000).
The second line contains a binary string representing the received word. Its length is either n-1, n, or n+1.

outputFormat

Output the recovered original binary word of length n that satisfies the specified property.

sample

4
1011

1001