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
#include<iostream>
using namespace std;

int calc(int a,int i){
	if(i==0 || i==4) return a;
	if(i==1 || i==3) return a>0?a%2:2;
	else return a%2==0;
}

int main(){
	int l;
	cin >> l;
	int a[l];
	for(int i=0;i<l;i++) cin >> a[i];

	long dp[5][l+1];
	for(int i=0;i<5;i++) dp[i][0]=0;
	for(int i=1;i<=l;i++){
		for(int j=0;j<5;j++){
			int add=calc(a[i-1],j);
			dp[j][i]=dp[j][i-1]+add;
			for(int k=0;k<j;k++) dp[j][i]=min(dp[j][i],dp[k][i-1]+add);
		}
	}

	long ans=1e18;
	for(int i=0;i<5;i++) ans=min(ans,dp[i][l]);
	cout << ans << endl;
	return 0;
}
