Codeforce A. Minimum Binary Number

A. Minimum Binary Number

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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:

1. swap any pair of adjacent characters (for example, "101"  "110");
2. replace "11" with "1" (for example, "110"  "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.

Examples

input

Copy

4
1001

output

Copy

100

input

Copy

1
1

output

Copy

1

Note

In the first example you can obtain the answer by the following sequence of operations: "1001"  "1010"  "1100"  "100".

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

极其聪明的想法

数数

因为只要后面有1

就可以不断变换跑上来消除

特判  1 0

尤其感谢帅气大巨轮的奇思妙想

#include <iostream>
#include <cstdio>
using namespace std;
int main()
{
	int n;
	cin>>n;
	int sum=0;
	for(int i=1;i<=n;i++)
	{
		char a;
		cin>>a;
		if(a=='0') sum++;
	}
	if(sum==1&&n==1)
	{
		cout<<"0"<<endl;
		return 0;
	}
	cout<<"1";
	while(sum--)
		cout<<"0";
	cout<<endl;
	return 0;	
}