#include <bits/stdc++.h>
using namespace std;

long long cost(long long a,int b)
{
	if (b==0||b==4)
	{
		return a;
	}
	else if (b==1||b==3)
	{
		if (a==0LL)
		{
			return 2LL;
		}
		else if (a%2LL==1)
		{
			return 1LL;
		}
		else
		{
			return 0LL;
		}
	}
	else if (b==2)
	{
		if (a%2LL==1LL)
		{
			return 0LL;
		}
		else
		{
			return 1LL;
		}
	}
}

int main(int argc, char const *argv[])
{
	int l;
	cin>>l;
	long long a[l];
	for (int i = 0; i < l; ++i)
	{
		cin>>a[i];
	}
	long long dp[l+5][5];
	for (int i = 0; i < l+5; ++i)
	{
		for (int j = 0; j < 5; ++j)
		{
			dp[i][j]=1000000000000000LL;
		}
	}
	dp[0][0]=0LL;
	for (int i = 1; i <= l; ++i)
	{
		for (int j = 0; j < 5; ++j)
		{
			for (int k = 0; k <= j; ++k)
			{
				dp[i][j]=min(dp[i][j],dp[i-1][k]+cost(a[i-1],j));
			}
		}
	}
	long long ans=1000000000000000LL;
	for (int i = 0; i < 5; ++i)
	{
		ans=min(ans,dp[l][i]);
	}
	cout<<ans<<endl;
	return 0;
}

### 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 <bits/stdc++.h>
using namespace std;

long long cost(long long a,int b)
{
	if (b==0||b==4)
	{
		return a;
	}
	else if (b==1||b==3)
	{
		if (a==0LL)
		{
			return 2LL;
		}
		else if (a%2LL==1)
		{
			return 1LL;
		}
		else
		{
			return 0LL;
		}
	}
	else if (b==2)
	{
		if (a%2LL==1LL)
		{
			return 0LL;
		}
		else
		{
			return 1LL;
		}
	}
}

int main(int argc, char const *argv[])
{
	int l;
	cin>>l;
	long long a[l];
	for (int i = 0; i < l; ++i)
	{
		cin>>a[i];
	}
	long long dp[l+5][5];
	for (int i = 0; i < l+5; ++i)
	{
		for (int j = 0; j < 5; ++j)
		{
			dp[i][j]=1000000000000000LL;
		}
	}
	dp[0][0]=0LL;
	for (int i = 1; i <= l; ++i)
	{
		for (int j = 0; j < 5; ++j)
		{
			for (int k = 0; k <= j; ++k)
			{
				dp[i][j]=min(dp[i][j],dp[i-1][k]+cost(a[i-1],j));
			}
		}
	}
	long long ans=1000000000000000LL;
	for (int i = 0; i < 5; ++i)
	{
		ans=min(ans,dp[l][i]);
	}
	cout<<ans<<endl;
	return 0;
}

```