#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define pa pair<int,int>
const int Maxn=200010;
const int inf=2147483647;
int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
	return x*f;
}
LL n,a[Maxn],f[Maxn],g[Maxn];
int main()
{
	n=read();
	for(int i=1;i<=n;i++)a[i]=read();
	f[0]=g[n+1]=0;
	LL o=0;
	for(int i=1;i<=n;i++)
	{
		o+=a[i];
		f[i]=min(f[i-1]+(a[i]&1)+(a[i]==0?2:0),o);
	}
	for(int i=1;i<=n;i++)f[i]=min(f[i-1]+(!(a[i]&1)),f[i]);
	o=0;
	for(int i=n;i;i--)
	{
		o+=a[i];
		g[i]=min(g[i+1]+(a[i]&1)+(a[i]==0?2:0),o);
	}
	LL ans=inf;
	for(int i=0;i<=n;i++)ans=min(ans,f[i]+g[i+1])/*,printf("%d %lld %lld\n",i,f[i],g[i+1])*/;
	printf("%lld",ans);
}
### Prompt

Develop a solution in Cpp 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<bits/stdc++.h>
using namespace std;
#define LL long long
#define pa pair<int,int>
const int Maxn=200010;
const int inf=2147483647;
int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
	return x*f;
}
LL n,a[Maxn],f[Maxn],g[Maxn];
int main()
{
	n=read();
	for(int i=1;i<=n;i++)a[i]=read();
	f[0]=g[n+1]=0;
	LL o=0;
	for(int i=1;i<=n;i++)
	{
		o+=a[i];
		f[i]=min(f[i-1]+(a[i]&1)+(a[i]==0?2:0),o);
	}
	for(int i=1;i<=n;i++)f[i]=min(f[i-1]+(!(a[i]&1)),f[i]);
	o=0;
	for(int i=n;i;i--)
	{
		o+=a[i];
		g[i]=min(g[i+1]+(a[i]&1)+(a[i]==0?2:0),o);
	}
	LL ans=inf;
	for(int i=0;i<=n;i++)ans=min(ans,f[i]+g[i+1])/*,printf("%d %lld %lld\n",i,f[i],g[i+1])*/;
	printf("%lld",ans);
}
```