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<bits/stdc++.h>
using namespace std;

typedef long long ll;
int l,a[200005];
ll f[200005][5];

void upd(ll &x,ll y){if(x>y)x=y;}

int cost(int x,int y){
	if(x==-1)return y;
	if(x==0)return y==0?2:y%2;
	return 1-y%2;
}

int main(){
	scanf("%d",&l);
	for(int i=1;i<=l;i++)scanf("%d",a+i);
	memset(f,0x3f,sizeof f);
	f[0][0]=0;
	for(int i=0;i<l;i++)
		for(int j=0;j<5;j++)
			for(int k=j;k<5;k++)
				upd(f[i+1][k],f[i][j]+cost(k==0||k==4?-1:k==1||k==3?0:1,a[i+1]));
	printf("%lld\n",min({f[l][0],f[l][1],f[l][2],f[l][3],f[l][4]}));
	return 0;
}
