Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions:

* He never visits a point with coordinate less than 0, or a point with coordinate greater than L.
* He starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate.
* He only changes direction at a point with integer coordinate.



Each time when Snuke passes a point with coordinate i-0.5, where i is an integer, he put a stone in his i-th ear.

After Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i, Snuke's i-th ear contains A_i stones:

* Put a stone in one of Snuke's ears.
* Remove a stone from one of Snuke's ears.



Find the minimum number of operations required when Ringo can freely decide how Snuke walks.

Constraints

* 1 \leq L \leq 2\times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq L)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


L
A_1
:
A_L


Output

Print the minimum number of operations required when Ringo can freely decide how Snuke walks.

Examples

Input

4
1
0
2
3


Output

1


Input

8
2
0
0
2
1
3
4
1


Output

3


Input

7
314159265
358979323
846264338
327950288
419716939
937510582
0


Output

1
import java.util.*;
public class Main {
	public static long value(int x,int j) {
		if (j==0||j==4) return x;
		if (j==2) return (x+1)%2;
		if (x==0) return 2;
		return x%2;
	}
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int L=in.nextInt();
		int[] A=new int[L+1];
		for (int i=1;i<=L;++i)
			A[i]=in.nextInt();
		long[][] dp=new long[L+1][5];
		for (int i=1;i<=L;++i)
			for (int j=0;j<5;++j)
				dp[i][j]=Long.MAX_VALUE;
		for (int i=0;i<L;++i)
			for (int j=0;j<5;++j) if (dp[i][j]!=Long.MAX_VALUE) {
				if (j+1<5) dp[i][j+1]=Math.min(dp[i][j+1],dp[i][j]);
				dp[i+1][j]=Math.min(dp[i+1][j],dp[i][j]+value(A[i+1],j));
			}
		long res=Long.MAX_VALUE;
		for (int i=0;i<5;++i) res=Math.min(res,dp[L][i]);
		System.out.println(res);
	}
}