#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#define llong long long
using namespace std;

const int N = 2e5;
llong a[N+3];
int b[N+3];
llong dp[N+3][5];
int n;

int eval(int x,int y,int id)
{
	if(x==0 || x==4)
	{
		return a[id];
	}
	else if(x==1 || x==3)
	{
		return 2-y;
	}
	else if(x==2)
	{
		return y==1 ? 0 : 1;
	}
}

int main()
{
	scanf("%d",&n);
	for(int i=1; i<=n; i++) scanf("%lld",&a[i]);
	for(int i=1; i<=n; i++)
	{
		if(a[i]==0) b[i] = 0;
		else if(a[i]&1) b[i] = 1;
		else b[i] = 2;
	}
	memset(dp,42,sizeof(dp));
	for(int i=0; i<=4; i++) dp[0][i] = 0ll;
	for(int i=1; i<=n; i++)
	{
		for(int j=0; j<=4; j++)
		{
			for(int k=0; k<=j; k++)
			{
				dp[i][j] = min(dp[i][j],dp[i-1][k]+eval(j,b[i],i));
			}
		}
	}
	llong ans = min(min(min(dp[n][0],dp[n][1]),dp[n][2]),min(dp[n][3],dp[n][4]));
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Please formulate 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<cstdlib>
#include<cstring>
#include<algorithm>
#define llong long long
using namespace std;

const int N = 2e5;
llong a[N+3];
int b[N+3];
llong dp[N+3][5];
int n;

int eval(int x,int y,int id)
{
	if(x==0 || x==4)
	{
		return a[id];
	}
	else if(x==1 || x==3)
	{
		return 2-y;
	}
	else if(x==2)
	{
		return y==1 ? 0 : 1;
	}
}

int main()
{
	scanf("%d",&n);
	for(int i=1; i<=n; i++) scanf("%lld",&a[i]);
	for(int i=1; i<=n; i++)
	{
		if(a[i]==0) b[i] = 0;
		else if(a[i]&1) b[i] = 1;
		else b[i] = 2;
	}
	memset(dp,42,sizeof(dp));
	for(int i=0; i<=4; i++) dp[0][i] = 0ll;
	for(int i=1; i<=n; i++)
	{
		for(int j=0; j<=4; j++)
		{
			for(int k=0; k<=j; k++)
			{
				dp[i][j] = min(dp[i][j],dp[i-1][k]+eval(j,b[i],i));
			}
		}
	}
	llong ans = min(min(min(dp[n][0],dp[n][1]),dp[n][2]),min(dp[n][3],dp[n][4]));
	printf("%lld\n",ans);
	return 0;
}
```