#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int gi(){
	int x=0,w=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')w=0,ch=getchar();
	while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return w?x:-x;
}
#define ll long long
const int N=2e5+5;
int n;ll a[N],x[N],y[N],L[N],R[N];
int main(){
	n=gi();
	for(int i=1;i<=n;++i){
		a[i]=gi(),x[i]=~a[i]&1,y[i]=a[i]?a[i]&1:2;
		a[i]+=a[i-1],x[i]+=x[i-1],y[i]+=y[i-1];
	}
	ll mn=0;
	for(int i=1;i<=n;++i)mn=min(mn,a[i]-y[i]),L[i]=mn+y[i];
	mn=y[n];
	for(int i=n-1;~i;--i)mn=min(mn,a[n]-a[i]+y[i]),R[i]=mn-y[i];
	ll ans=1ll<<60;mn=1ll<<60;
	for(int i=0;i<=n;++i)mn=min(mn,L[i]-x[i]),ans=min(ans,mn+R[i]+x[i]);
	printf("%lld\n",ans);return 0;
}

### Prompt

Generate a Cpp solution to 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<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int gi(){
	int x=0,w=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')w=0,ch=getchar();
	while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return w?x:-x;
}
#define ll long long
const int N=2e5+5;
int n;ll a[N],x[N],y[N],L[N],R[N];
int main(){
	n=gi();
	for(int i=1;i<=n;++i){
		a[i]=gi(),x[i]=~a[i]&1,y[i]=a[i]?a[i]&1:2;
		a[i]+=a[i-1],x[i]+=x[i-1],y[i]+=y[i-1];
	}
	ll mn=0;
	for(int i=1;i<=n;++i)mn=min(mn,a[i]-y[i]),L[i]=mn+y[i];
	mn=y[n];
	for(int i=n-1;~i;--i)mn=min(mn,a[n]-a[i]+y[i]),R[i]=mn-y[i];
	ll ans=1ll<<60;mn=1ll<<60;
	for(int i=0;i<=n;++i)mn=min(mn,L[i]-x[i]),ans=min(ans,mn+R[i]+x[i]);
	printf("%lld\n",ans);return 0;
}

```