#include <iostream>
#include <vector>
#include <map>
#include <algorithm>
#include <queue>
using namespace std;

int L;

int main() {
    cin >> L;
    vector<vector<long long>> dp(L + 1, vector<long long>(5));
    for (int i = 0; i < L; i++) {
        int a;
        cin >> a;
        dp[i + 1][0] = dp[i][0] + a;
        long long m = min(dp[i][0], dp[i][1]);
        int even = a == 0? 2: a % 2;
        dp[i + 1][1] = m + even;
        m = min(m, dp[i][2]);
        dp[i + 1][2] = m + (a + 1) % 2;
        m = min(m, dp[i][3]);
        dp[i + 1][3] = m + even;
        m = min(m, dp[i][4]);
        dp[i + 1][4] = m + a;
    }
    long long ans = dp[L][0];
    for (int i = 1; i < 5; i++) {
        ans = min(ans, dp[L][i]);
    }
    cout << ans << endl;
}
### Prompt

Your task is to create 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 <iostream>
#include <vector>
#include <map>
#include <algorithm>
#include <queue>
using namespace std;

int L;

int main() {
    cin >> L;
    vector<vector<long long>> dp(L + 1, vector<long long>(5));
    for (int i = 0; i < L; i++) {
        int a;
        cin >> a;
        dp[i + 1][0] = dp[i][0] + a;
        long long m = min(dp[i][0], dp[i][1]);
        int even = a == 0? 2: a % 2;
        dp[i + 1][1] = m + even;
        m = min(m, dp[i][2]);
        dp[i + 1][2] = m + (a + 1) % 2;
        m = min(m, dp[i][3]);
        dp[i + 1][3] = m + even;
        m = min(m, dp[i][4]);
        dp[i + 1][4] = m + a;
    }
    long long ans = dp[L][0];
    for (int i = 1; i < 5; i++) {
        ans = min(ans, dp[L][i]);
    }
    cout << ans << endl;
}
```