#include <bits/stdc++.h>
using namespace std;
int main() {
    long long INF = 1LL << 60;
    int L;
    cin >> L;
    long long a;
    vector<vector<long long>> c(5,vector<long long>(L+2));
    vector<vector<long long>> dp(5,vector<long long>(L+2, INF));
    for(int i=1; i<=L; i++) {
        cin >> a;
        c[0][i] = c[4][i] = a;
        c[1][i] = c[3][i] = a==0 ? 2 : a%2;
        c[2][i] = (a+1)%2;
    }
    dp[0][0] = 0;
    for (int k=0; k<5; k++) {
        for (int i=1;i<=L+1;i++) {
            for (int j=0; j<=k; j++) {
                dp[k][i] = min(dp[k][i], dp[k-j][i-1] + c[k][i]);
            }
        }
    }
    cout << dp[4][L+1] << '\n';
    return 0;
}
### Prompt

Generate 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 <bits/stdc++.h>
using namespace std;
int main() {
    long long INF = 1LL << 60;
    int L;
    cin >> L;
    long long a;
    vector<vector<long long>> c(5,vector<long long>(L+2));
    vector<vector<long long>> dp(5,vector<long long>(L+2, INF));
    for(int i=1; i<=L; i++) {
        cin >> a;
        c[0][i] = c[4][i] = a;
        c[1][i] = c[3][i] = a==0 ? 2 : a%2;
        c[2][i] = (a+1)%2;
    }
    dp[0][0] = 0;
    for (int k=0; k<5; k++) {
        for (int i=1;i<=L+1;i++) {
            for (int j=0; j<=k; j++) {
                dp[k][i] = min(dp[k][i], dp[k-j][i-1] + c[k][i]);
            }
        }
    }
    cout << dp[4][L+1] << '\n';
    return 0;
}
```