#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define rep(i,l,r) for (int i=(l); i<=(r); i++)
typedef long long ll;
using namespace std;

const int N=200010;
int n,a[N];
ll ans,sm1[N],sm2[N],sm3[N],mn1[N],mn2[N],mn3[N];

int main(){
	scanf("%d",&n);
	rep(i,1,n) scanf("%d",&a[i]),ans+=a[i];
	rep(i,1,n) sm1[i]=sm1[i-1]+a[i];
	rep(i,1,n) sm2[i]=sm2[i-1]+((a[i]&1)?1:(a[i]?0:2));
	rep(i,1,n) sm3[i]=sm3[i-1]+(!(a[i]&1));
	rep(i,1,n) mn1[i]=min(mn1[i-1],sm1[i]-sm2[i]);
	rep(i,1,n) mn2[i]=min(mn2[i-1],sm2[i]+mn1[i]-sm3[i]);
	rep(i,1,n) mn3[i]=min(mn3[i-1],sm3[i]+mn2[i]-sm2[i]);
	rep(i,0,n) ans=min(ans,sm2[i]+mn3[i]+sm1[n]-sm1[i]);
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Your task is to create 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<cstring>
#include<iostream>
#include<algorithm>
#define rep(i,l,r) for (int i=(l); i<=(r); i++)
typedef long long ll;
using namespace std;

const int N=200010;
int n,a[N];
ll ans,sm1[N],sm2[N],sm3[N],mn1[N],mn2[N],mn3[N];

int main(){
	scanf("%d",&n);
	rep(i,1,n) scanf("%d",&a[i]),ans+=a[i];
	rep(i,1,n) sm1[i]=sm1[i-1]+a[i];
	rep(i,1,n) sm2[i]=sm2[i-1]+((a[i]&1)?1:(a[i]?0:2));
	rep(i,1,n) sm3[i]=sm3[i-1]+(!(a[i]&1));
	rep(i,1,n) mn1[i]=min(mn1[i-1],sm1[i]-sm2[i]);
	rep(i,1,n) mn2[i]=min(mn2[i-1],sm2[i]+mn1[i]-sm3[i]);
	rep(i,1,n) mn3[i]=min(mn3[i-1],sm3[i]+mn2[i]-sm2[i]);
	rep(i,0,n) ans=min(ans,sm2[i]+mn3[i]+sm1[n]-sm1[i]);
	printf("%lld\n",ans);
	return 0;
}
```