#include <iostream>
using namespace std;
typedef long long ll;
ll L,A[200010];
ll dp[200010][5] = {};

int main(){
	cin >> L;
	for(int i=1;i<=L;i++){
		cin >> A[i];
	}
	for(int i=0;i<=L;i++){
		for(int j=0;j<5;j++){
			dp[i][j] = 1e18;
		}
	}
	dp[0][0] = 0;
	dp[0][1] = 0;
	for(int i=1;i<=L;i++){
		int c = 0;
		if(A[i]%2==1) c = 1;
		else if(A[i]==0) c = 2;
		dp[i][0] = dp[i-1][0]+A[i];
		dp[i][1] = min(dp[i-1][0],dp[i-1][1])+c;
		dp[i][2] = min(min(dp[i-1][1],dp[i-1][2]),dp[i-1][0])+(A[i]%2==0);
		dp[i][3] = min(min(dp[i-1][2],dp[i-1][3]),dp[i-1][0])+c;
		dp[i][4] = min(min(dp[i-1][3],dp[i-1][4]),dp[i-1][2])+A[i];
	}
	ll ans = 1e18;
	for(int j=0;j<5;j++) ans = min(ans,dp[L][j]);
	cout << ans << endl;
}
### Prompt

Please create a solution in CPP 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 <iostream>
using namespace std;
typedef long long ll;
ll L,A[200010];
ll dp[200010][5] = {};

int main(){
	cin >> L;
	for(int i=1;i<=L;i++){
		cin >> A[i];
	}
	for(int i=0;i<=L;i++){
		for(int j=0;j<5;j++){
			dp[i][j] = 1e18;
		}
	}
	dp[0][0] = 0;
	dp[0][1] = 0;
	for(int i=1;i<=L;i++){
		int c = 0;
		if(A[i]%2==1) c = 1;
		else if(A[i]==0) c = 2;
		dp[i][0] = dp[i-1][0]+A[i];
		dp[i][1] = min(dp[i-1][0],dp[i-1][1])+c;
		dp[i][2] = min(min(dp[i-1][1],dp[i-1][2]),dp[i-1][0])+(A[i]%2==0);
		dp[i][3] = min(min(dp[i-1][2],dp[i-1][3]),dp[i-1][0])+c;
		dp[i][4] = min(min(dp[i-1][3],dp[i-1][4]),dp[i-1][2])+A[i];
	}
	ll ans = 1e18;
	for(int j=0;j<5;j++) ans = min(ans,dp[L][j]);
	cout << ans << endl;
}
```