#include <iostream>
#include <algorithm>

using namespace std;

long dp[200000][5];

long calc_even(long n){
    if(n == 0) return 2;
    else return (n)%2;
}

int main(){
    int L;
    long A[200000];
    cin >> L;
    for(int i = 0; i < L; i++) cin >> A[i];
    dp[0][0] = A[0];
    dp[0][1] = calc_even(A[0]);
    dp[0][2] = (A[0]+1)%2;
    dp[0][3] = calc_even(A[0]);
    dp[0][4] = A[0];
    for(int i = 1; i < L; i++){
        dp[i][0] = dp[i-1][0]+A[i];
        dp[i][1] = min(dp[i-1][0], dp[i-1][1])+calc_even(A[i]);
        dp[i][2] = min({dp[i-1][0], dp[i-1][1], dp[i-1][2]}) + (A[i]+1)%2;
        dp[i][3] = min({dp[i-1][0], dp[i-1][1], dp[i-1][2], dp[i-1][3]})+calc_even(A[i]);
        dp[i][4] = min({dp[i-1][0], dp[i-1][1], dp[i-1][2], dp[i-1][3], dp[i-1][4]})+A[i];
    }
    cout << min({dp[L-1][0], dp[L-1][1], dp[L-1][2], dp[L-1][3], dp[L-1][4]}) << 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>
#include <algorithm>

using namespace std;

long dp[200000][5];

long calc_even(long n){
    if(n == 0) return 2;
    else return (n)%2;
}

int main(){
    int L;
    long A[200000];
    cin >> L;
    for(int i = 0; i < L; i++) cin >> A[i];
    dp[0][0] = A[0];
    dp[0][1] = calc_even(A[0]);
    dp[0][2] = (A[0]+1)%2;
    dp[0][3] = calc_even(A[0]);
    dp[0][4] = A[0];
    for(int i = 1; i < L; i++){
        dp[i][0] = dp[i-1][0]+A[i];
        dp[i][1] = min(dp[i-1][0], dp[i-1][1])+calc_even(A[i]);
        dp[i][2] = min({dp[i-1][0], dp[i-1][1], dp[i-1][2]}) + (A[i]+1)%2;
        dp[i][3] = min({dp[i-1][0], dp[i-1][1], dp[i-1][2], dp[i-1][3]})+calc_even(A[i]);
        dp[i][4] = min({dp[i-1][0], dp[i-1][1], dp[i-1][2], dp[i-1][3], dp[i-1][4]})+A[i];
    }
    cout << min({dp[L-1][0], dp[L-1][1], dp[L-1][2], dp[L-1][3], dp[L-1][4]}) << endl;
}
```