Alice has a binary string. She thinks a binary string is beautiful if and only if it doesn't contain the substring $\text{"010"}$.

In one step, Alice can change a $0$ to a $1$ or vice versa. Count and print the minimum number of steps needed to make Alice see the string as beautiful.

Example

$b=\textbf{010}$

She can change any one element and have a beautiful string.

Function Description

Complete the beautifulBinaryString function in the editor below.

beautifulBinaryString has the following parameter(s):

string b: a string of binary digits

Returns

int: the minimum moves required

Input Format

The first line contains an integer $n$, the length of binary string.

The second line contains a single binary string $\boldsymbol{b}$.

Constraints

$1\leq n\leq100$
$b[i]\in\{0,1\}$.

Output Format

Print the minimum number of steps needed to make the string beautiful.

Sample Input 0

STDIN Function
----- --------
7 length of string n = 7
0101010 b = '0101010'

Sample Output 0

2

Explanation 0:

In this sample, $b=\text{"0101010"}$

The figure below shows a way to get rid of each instance of $\text{"010"}$:

Make the string beautiful by changing $2$ characters ($b[2]$ and $b\left[5\right]$).

Sample Input 1

5
01100

Sample Output 1

0

Sample Case 1:

In this sample $b=\text{"01100"}$

Explanation 1

The substring $\text{"010"}$ does not occur in $\boldsymbol{b}$, so the string is already beautiful in $0$ moves.

Sample Input 2

10
0100101010

Sample Output 2

3

Explanation 2

In this sample $b=\text{"0100101010"}$

One solution is to change the values of $b[2],b[5]\:\text{and}\:b[9]$ to form a beautiful string.

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