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

#define MAX 1000000

int main(){
    int l;
    cin >> l;

    vector<long long> a(l+1, 0);
    for (int i=1;i<l+1;i++){
        cin >> a[i];
    }

    vector<vector<long long>> dp;
    dp.resize(l+1);
    for (int i=0;i<l+1;i++){
        dp[i].resize(5);
    }

    for (int t=1;t<5;t++){
        dp[0][t] = 0;
    }

    for (int i=1;i<l+1;i++){
        int c;
        if (a[i]==0){c = 2;}
        else{c = 0;}
        dp[i][0] = dp[i-1][0] + a[i];
        dp[i][1] = min(dp[i-1][0], dp[i-1][1])+a[i]%2+c;
        dp[i][2] = min(min(dp[i-1][0], dp[i-1][1]), dp[i-1][2])+1-a[i]%2;
        dp[i][3] = min(dp[i-1][2], dp[i-1][3])+a[i]%2+c;
        dp[i][4] = min(dp[i-1][1], min(dp[i-1][2], min(dp[i-1][3], dp[i-1][4])))+a[i];
    }
    
    cout << *min_element(dp[l].begin(), dp[l].end()) << endl;
}

### 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;

#define MAX 1000000

int main(){
    int l;
    cin >> l;

    vector<long long> a(l+1, 0);
    for (int i=1;i<l+1;i++){
        cin >> a[i];
    }

    vector<vector<long long>> dp;
    dp.resize(l+1);
    for (int i=0;i<l+1;i++){
        dp[i].resize(5);
    }

    for (int t=1;t<5;t++){
        dp[0][t] = 0;
    }

    for (int i=1;i<l+1;i++){
        int c;
        if (a[i]==0){c = 2;}
        else{c = 0;}
        dp[i][0] = dp[i-1][0] + a[i];
        dp[i][1] = min(dp[i-1][0], dp[i-1][1])+a[i]%2+c;
        dp[i][2] = min(min(dp[i-1][0], dp[i-1][1]), dp[i-1][2])+1-a[i]%2;
        dp[i][3] = min(dp[i-1][2], dp[i-1][3])+a[i]%2+c;
        dp[i][4] = min(dp[i-1][1], min(dp[i-1][2], min(dp[i-1][3], dp[i-1][4])))+a[i];
    }
    
    cout << *min_element(dp[l].begin(), dp[l].end()) << endl;
}

```