#include<bits/stdc++.h>
#define ll long long
#define rg register
using namespace std;
const int MAXN=2e5+10;
ll Ans,n,Seq[MAXN],Pre[MAXN],Odd[MAXN],Even[MAXN];
ll Dp[MAXN][4];
inline ll Min(rg ll A,rg ll B){   return A<B?A:B;   }
int main()
{   memset(Dp,0X7f,sizeof(Dp));
	scanf("%lld",&n),Dp[0][0]=0;
	for(rg int i=1;i<=n;i++) scanf("%lld",&Seq[i]),Ans+=Seq[i];
	for(rg int i=1;i<=n;i++) Odd[i]=(Seq[i]&1),Even[i]=(Seq[i]&&(~Seq[i]&1));
	for(rg int i=1;i<=n;i++)
	{	Dp[i][0]=Dp[i-1][0]+Seq[i];
		Dp[i][1]=Min(Dp[i-1][1],Dp[i-1][0])+(Seq[i]?!Even[i]:2);
		Dp[i][2]=Min(Dp[i-1][2],Min(Dp[i-1][1],Dp[i-1][0]))+(!Odd[i]);
		Dp[i][3]=Min(Dp[i-1][3],Min(Dp[i-1][2],Min(Dp[i-1][1],Dp[i-1][0])))+(Seq[i]?!Even[i]:2);
	}
	for(rg ll i=n,Sum=0;i>=1;i--) Ans=Min(Ans,Min(Dp[i][3],Dp[i][2])+Sum),Sum+=Seq[i];
	printf("%lld\n",Ans);
}

### 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<bits/stdc++.h>
#define ll long long
#define rg register
using namespace std;
const int MAXN=2e5+10;
ll Ans,n,Seq[MAXN],Pre[MAXN],Odd[MAXN],Even[MAXN];
ll Dp[MAXN][4];
inline ll Min(rg ll A,rg ll B){   return A<B?A:B;   }
int main()
{   memset(Dp,0X7f,sizeof(Dp));
	scanf("%lld",&n),Dp[0][0]=0;
	for(rg int i=1;i<=n;i++) scanf("%lld",&Seq[i]),Ans+=Seq[i];
	for(rg int i=1;i<=n;i++) Odd[i]=(Seq[i]&1),Even[i]=(Seq[i]&&(~Seq[i]&1));
	for(rg int i=1;i<=n;i++)
	{	Dp[i][0]=Dp[i-1][0]+Seq[i];
		Dp[i][1]=Min(Dp[i-1][1],Dp[i-1][0])+(Seq[i]?!Even[i]:2);
		Dp[i][2]=Min(Dp[i-1][2],Min(Dp[i-1][1],Dp[i-1][0]))+(!Odd[i]);
		Dp[i][3]=Min(Dp[i-1][3],Min(Dp[i-1][2],Min(Dp[i-1][1],Dp[i-1][0])))+(Seq[i]?!Even[i]:2);
	}
	for(rg ll i=n,Sum=0;i>=1;i--) Ans=Min(Ans,Min(Dp[i][3],Dp[i][2])+Sum),Sum+=Seq[i];
	printf("%lld\n",Ans);
}

```