#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#define ll long long
using namespace std;
template <class T>
inline void read(T &x)
{
    x=0; char c=getchar();  int f=1;
    while(!isdigit(c)){if(c=='-')f=-1; c=getchar();}
    while(isdigit(c)) x=x*10-'0'+c,c=getchar(); x*=f;
}
const int N=2e5+10;
ll pre[N][5];
int n,a[N];
int main()
{
//	freopen("in.txt","r",stdin);
	read(n);
	for(int i=1;i<=n;++i) read(a[i]);
	ll ans=1e18;
	for(int i=1;i<=n;++i)
	{
		pre[i][0]=pre[i-1][0];
		for(int j=1;j<5;++j) pre[i][j]=min(pre[i][j-1],pre[i-1][j]);
		pre[i][0]+=a[i];
		pre[i][1]+=(a[i]==0?2:a[i]%2);
		pre[i][2]+=(a[i]%2==0);
		pre[i][3]+=(a[i]==0?2:a[i]%2);
		pre[i][4]+=a[i];
	}
	for(int j=0;j<5;++j) ans=min(ans,pre[n][j]);
	printf("%lld",ans);
	return 0;
}	
### Prompt

Please provide a CPP coded solution to the problem described below:

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 <iostream>
#include <cstring>
#include <algorithm>
#define ll long long
using namespace std;
template <class T>
inline void read(T &x)
{
    x=0; char c=getchar();  int f=1;
    while(!isdigit(c)){if(c=='-')f=-1; c=getchar();}
    while(isdigit(c)) x=x*10-'0'+c,c=getchar(); x*=f;
}
const int N=2e5+10;
ll pre[N][5];
int n,a[N];
int main()
{
//	freopen("in.txt","r",stdin);
	read(n);
	for(int i=1;i<=n;++i) read(a[i]);
	ll ans=1e18;
	for(int i=1;i<=n;++i)
	{
		pre[i][0]=pre[i-1][0];
		for(int j=1;j<5;++j) pre[i][j]=min(pre[i][j-1],pre[i-1][j]);
		pre[i][0]+=a[i];
		pre[i][1]+=(a[i]==0?2:a[i]%2);
		pre[i][2]+=(a[i]%2==0);
		pre[i][3]+=(a[i]==0?2:a[i]%2);
		pre[i][4]+=a[i];
	}
	for(int j=0;j<5;++j) ans=min(ans,pre[n][j]);
	printf("%lld",ans);
	return 0;
}	
```