#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#include <vector>
#include <utility>
#define maxn 200005
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
int n,a[maxn];
ll f[maxn][7];
int main(){
	scanf("%d",&n);
	for(int i = 1;i <= n;i++) scanf("%d",&a[i]);
	for(int i = 1;i <= n;i++){
		f[i][1] = f[i - 1][1];
		f[i][2] = min(f[i - 1][2],f[i][1]);
		f[i][3] = min(f[i - 1][3],f[i][2]);
		f[i][4] = min(f[i - 1][4],f[i][3]);
		f[i][5] = min(f[i - 1][5],f[i][4]);
		f[i][1] += a[i];
		if(a[i] == 0) f[i][2] += 2;
		else f[i][2] += a[i] & 1;
		f[i][3] += 1 - (a[i] & 1);
		if(a[i] == 0) f[i][4] += 2;
		else f[i][4] += a[i] & 1;
		f[i][5] += a[i];
	}
	ll res = 0x3f3f3f3f;
	for(int i = 1;i <= 5;i++) res = min(res,f[n][i]);
	printf("%lld\n",res);
	return 0;
}

### 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 <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#include <vector>
#include <utility>
#define maxn 200005
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
int n,a[maxn];
ll f[maxn][7];
int main(){
	scanf("%d",&n);
	for(int i = 1;i <= n;i++) scanf("%d",&a[i]);
	for(int i = 1;i <= n;i++){
		f[i][1] = f[i - 1][1];
		f[i][2] = min(f[i - 1][2],f[i][1]);
		f[i][3] = min(f[i - 1][3],f[i][2]);
		f[i][4] = min(f[i - 1][4],f[i][3]);
		f[i][5] = min(f[i - 1][5],f[i][4]);
		f[i][1] += a[i];
		if(a[i] == 0) f[i][2] += 2;
		else f[i][2] += a[i] & 1;
		f[i][3] += 1 - (a[i] & 1);
		if(a[i] == 0) f[i][4] += 2;
		else f[i][4] += a[i] & 1;
		f[i][5] += a[i];
	}
	ll res = 0x3f3f3f3f;
	for(int i = 1;i <= 5;i++) res = min(res,f[n][i]);
	printf("%lld\n",res);
	return 0;
}

```