#include <iostream>
#include <vector>

using namespace std;

int main(){
    int L;
    while(cin >> L){
        vector<int> A(L);
        for(auto& t : A) cin >> t;
        vector<vector<long long>> dp(5, vector<long long>(L+1, 1LL << 60));
        dp[0][0] = 0;
        for(int i=0;i<L;i++){
            long long base = dp[0][i];
            dp[0][i+1] = dp[0][i] + A[i];
            base = min(base, dp[1][i]);
            dp[1][i+1] = base + (A[i] == 0 ? 2 : A[i]%2 == 1 ? 1 : 0);
            base = min(base, dp[2][i]);
            dp[2][i+1] = base + (A[i]%2 == 0 ? 1 : 0);
            base = min(base, dp[3][i]);
            dp[3][i+1] = base + (A[i] == 0 ? 2 : A[i]%2 == 1 ? 1 : 0);
            base = min(base, dp[4][i]);
            dp[4][i+1] = base + A[i];
        }
        long long res = dp[0][L];
        for(int i=1;i<5;i++) res = min(res, dp[i][L]);
        cout << res << endl;
    }
}
### Prompt

In cpp, your task is to solve 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>

using namespace std;

int main(){
    int L;
    while(cin >> L){
        vector<int> A(L);
        for(auto& t : A) cin >> t;
        vector<vector<long long>> dp(5, vector<long long>(L+1, 1LL << 60));
        dp[0][0] = 0;
        for(int i=0;i<L;i++){
            long long base = dp[0][i];
            dp[0][i+1] = dp[0][i] + A[i];
            base = min(base, dp[1][i]);
            dp[1][i+1] = base + (A[i] == 0 ? 2 : A[i]%2 == 1 ? 1 : 0);
            base = min(base, dp[2][i]);
            dp[2][i+1] = base + (A[i]%2 == 0 ? 1 : 0);
            base = min(base, dp[3][i]);
            dp[3][i+1] = base + (A[i] == 0 ? 2 : A[i]%2 == 1 ? 1 : 0);
            base = min(base, dp[4][i]);
            dp[4][i+1] = base + A[i];
        }
        long long res = dp[0][L];
        for(int i=1;i<5;i++) res = min(res, dp[i][L]);
        cout << res << endl;
    }
}
```