#include<iostream>
#include<algorithm>
#define int long long
using namespace std;
const int N=2e5+10;
int n,A[N],suma[N],sumb[N],sumc[N],L[N],R[N];
int ss[N],sumL[N],Ans=1e18;
void Get(int *sa,int *sb,int *val)
{
	int p=0;
	for(int i=1;i<=n;i++)
	{
		ss[i]=sa[i]-sb[i];
		if(ss[i]<ss[p]) p=i;
		val[i]=sb[i]+ss[p];
	}
}
signed main()
{
	cin>>n;
	for(int i=1;i<=n;i++) cin>>A[i];
	//Get L
	for(int i=1;i<=n;i++)
	{
		suma[i]=suma[i-1]+A[i];
		sumb[i]=sumb[i-1]+(A[i]==0?2:(A[i]&1));
	}
	Get(suma,sumb,L);
	
	//Get R
	reverse(A+1,A+n+1);	
	for(int i=1;i<=n;i++)
	{
		suma[i]=suma[i-1]+A[i];
		sumb[i]=sumb[i-1]+(A[i]==0?2:(A[i]&1));
	}
	Get(suma,sumb,R);
	reverse(R+1,R+n+1);
	reverse(A+1,A+n+1);
	
	//Get Ans
	for(int i=1;i<=n;i++)
		sumc[i]=sumc[i-1]+1-(A[i]&1);
	Get(L,sumc,sumL);
	for(int i=0;i<=n;i++)
		Ans=min(Ans,sumL[i]+R[i+1]);
	cout<<Ans<<endl;
}

### Prompt

In CPP, your task is to solve the following problem:

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

### Response

```cpp
#include<iostream>
#include<algorithm>
#define int long long
using namespace std;
const int N=2e5+10;
int n,A[N],suma[N],sumb[N],sumc[N],L[N],R[N];
int ss[N],sumL[N],Ans=1e18;
void Get(int *sa,int *sb,int *val)
{
	int p=0;
	for(int i=1;i<=n;i++)
	{
		ss[i]=sa[i]-sb[i];
		if(ss[i]<ss[p]) p=i;
		val[i]=sb[i]+ss[p];
	}
}
signed main()
{
	cin>>n;
	for(int i=1;i<=n;i++) cin>>A[i];
	//Get L
	for(int i=1;i<=n;i++)
	{
		suma[i]=suma[i-1]+A[i];
		sumb[i]=sumb[i-1]+(A[i]==0?2:(A[i]&1));
	}
	Get(suma,sumb,L);
	
	//Get R
	reverse(A+1,A+n+1);	
	for(int i=1;i<=n;i++)
	{
		suma[i]=suma[i-1]+A[i];
		sumb[i]=sumb[i-1]+(A[i]==0?2:(A[i]&1));
	}
	Get(suma,sumb,R);
	reverse(R+1,R+n+1);
	reverse(A+1,A+n+1);
	
	//Get Ans
	for(int i=1;i<=n;i++)
		sumc[i]=sumc[i-1]+1-(A[i]&1);
	Get(L,sumc,sumL);
	for(int i=0;i<=n;i++)
		Ans=min(Ans,sumL[i]+R[i+1]);
	cout<<Ans<<endl;
}

```