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;
const int N=2e5+5;
int a[N],n,i,j;
long long f[N][5],x;
int main(){
	scanf("%d",&n);
	f[0][1]=f[0][2]=f[0][3]=f[0][4]=1ll<<60;
	for(i=1;i<=n;++i){
		scanf("%d",a+i);
		f[i][0]=f[i-1][0]+a[i];
		f[i][1]=min(f[i-1][0],f[i-1][1])+(a[i]?a[i]%2:2);
		f[i][2]=min(f[i-1][0],min(f[i-1][1],f[i-1][2]))+1-a[i]%2;
		f[i][3]=min(min(f[i-1][0],f[i-1][1]),min(f[i-1][2],f[i-1][3]))+(a[i]?a[i]%2:2);
		f[i][4]=min(min(min(f[i-1][0],f[i-1][1]),min(f[i-1][2],f[i-1][3])),f[i-1][4])+a[i];
	}
	x=1ll<<60;
	for(j=0;j<5;++j)x=min(x,f[n][j]);
	cout<<x<<endl;
	return 0;
}