#include<iostream>
#include<algorithm>
using namespace std;
int n;
long dp[2<<17][5];
int main()
{
	cin>>n;
	for(int i=0;i++<n+1;)
	{
		long a=0;cin>>a;
		long now=9e18;
		for(int j=0;j<5;j++)
		{
			now=min(now,dp[i-1][j]);
			dp[i][j]=now+(j-2?j%2?a?a%2:2:a:1-a%2);
		}
	}
	cout<<dp[n+1][4]<<endl;
}

### 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<iostream>
#include<algorithm>
using namespace std;
int n;
long dp[2<<17][5];
int main()
{
	cin>>n;
	for(int i=0;i++<n+1;)
	{
		long a=0;cin>>a;
		long now=9e18;
		for(int j=0;j<5;j++)
		{
			now=min(now,dp[i-1][j]);
			dp[i][j]=now+(j-2?j%2?a?a%2:2:a:1-a%2);
		}
	}
	cout<<dp[n+1][4]<<endl;
}

```