// 600

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

    ll dp[5][200001];

int main(){
    int L;
    cin >> L;
    ll A[200001];
    for(int i=1;i<=L;i++) cin >> A[i];

    for(int i=0;i<5;i++)dp[i][0]=0;
    for(int i=1;i<=L;i++){
        dp[0][i]=dp[0][i-1]+A[i];

        if(A[i]==0) dp[1][i]=min(dp[0][i-1], dp[1][i-1])+2;
        else        dp[1][i]=min(dp[0][i-1], dp[1][i-1])+A[i]%2;

        dp[2][i]=min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1])+(A[i]+1)%2;

        dp[3][i]=min(min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1]),dp[3][i-1]);
        if(A[i]==0) dp[3][i] += 2;
        else dp[3][i] += A[i]%2;

        dp[4][i]=min(min(min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1]),dp[3][i-1]),dp[4][i-1])+A[i];
    }
    
    int i=L+1;
    cout << min(min(min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1]),dp[3][i-1]),dp[4][i-1]) << endl;
    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
// 600

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

    ll dp[5][200001];

int main(){
    int L;
    cin >> L;
    ll A[200001];
    for(int i=1;i<=L;i++) cin >> A[i];

    for(int i=0;i<5;i++)dp[i][0]=0;
    for(int i=1;i<=L;i++){
        dp[0][i]=dp[0][i-1]+A[i];

        if(A[i]==0) dp[1][i]=min(dp[0][i-1], dp[1][i-1])+2;
        else        dp[1][i]=min(dp[0][i-1], dp[1][i-1])+A[i]%2;

        dp[2][i]=min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1])+(A[i]+1)%2;

        dp[3][i]=min(min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1]),dp[3][i-1]);
        if(A[i]==0) dp[3][i] += 2;
        else dp[3][i] += A[i]%2;

        dp[4][i]=min(min(min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1]),dp[3][i-1]),dp[4][i-1])+A[i];
    }
    
    int i=L+1;
    cout << min(min(min(min(dp[0][i-1],dp[1][i-1]),dp[2][i-1]),dp[3][i-1]),dp[4][i-1]) << endl;
    return 0;
}
```