Minimum Binary Number

1000ms

262144K

Description:

String can be called correct if it consists of characters "0" and "1" and there are no redundant leading zeroes. Here are some examples: "0", "10", "1001".

You are given a correct string s.

You can perform two different operations on this string:

swap any pair of adjacent characters (for example, "101" $\text{[math]}$ "110");
replace "11" with "1" (for example, "110" $\text{[math]}$ "10").

Let val(s) be such a number that s is its binary representation.

Correct string a is less than some other correct string b iff val(a) < val(b).

Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all).

Input:

The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s.

The second line contains the string s consisting of characters "0" and "1". It is guaranteed that the string s is correct.

Output:

Print one string — the minimum correct string that you can obtain from the given one.

Sample Input:

4
1001

Sample Output:

Sample Input:

1
1

Sample Output:

Note:

In the first example you can obtain the answer by the following sequence of operations: "1001" $\text{[math]}$ "1010" $\text{[math]}$ "1100" $\text{[math]}$ "100".

In the second example you can't obtain smaller answer no matter what operations you use.

Informação

Provedor Codeforces

Código CF976A