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

#define watch(x) cerr << (#x) << ": " << (x) << endl
#define int long long



int32_t main() {

    int l; cin >> l;
    vector<int> a(l+1);
    for(int i = 1; i <= l; ++i) cin >> a[i];

    vector<vector<int>> dp(l+1, vector<int>(5, 0));

    for(int i = 1; i <= l; ++i) {
        int ai = a[i];
        dp[i][0] = dp[i-1][0] + ai;
        int e = ai%2 + (ai==0)*2;
        dp[i][1] = e + min(dp[i-1][0], dp[i-1][1]);
        int f = (ai+1)%2;
        dp[i][2] = f + min(dp[i-1][0], min(dp[i-1][1], dp[i-1][2]));
        dp[i][3] = e + min(dp[i-1][0], min(dp[i-1][1], min(dp[i-1][2], dp[i-1][3])));
        dp[i][4] = ai + min({dp[i-1][0], dp[i-1][1], dp[i-1][2], dp[i-1][3], dp[i-1][4]});
    }

    cout << min({dp[l][0], dp[l][1], dp[l][2], dp[l][3], dp[l][4]}) << endl;
    
    return 0;
}

### 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 <bits/stdc++.h>
using namespace std;

#define watch(x) cerr << (#x) << ": " << (x) << endl
#define int long long



int32_t main() {

    int l; cin >> l;
    vector<int> a(l+1);
    for(int i = 1; i <= l; ++i) cin >> a[i];

    vector<vector<int>> dp(l+1, vector<int>(5, 0));

    for(int i = 1; i <= l; ++i) {
        int ai = a[i];
        dp[i][0] = dp[i-1][0] + ai;
        int e = ai%2 + (ai==0)*2;
        dp[i][1] = e + min(dp[i-1][0], dp[i-1][1]);
        int f = (ai+1)%2;
        dp[i][2] = f + min(dp[i-1][0], min(dp[i-1][1], dp[i-1][2]));
        dp[i][3] = e + min(dp[i-1][0], min(dp[i-1][1], min(dp[i-1][2], dp[i-1][3])));
        dp[i][4] = ai + min({dp[i-1][0], dp[i-1][1], dp[i-1][2], dp[i-1][3], dp[i-1][4]});
    }

    cout << min({dp[l][0], dp[l][1], dp[l][2], dp[l][3], dp[l][4]}) << endl;
    
    return 0;
}

```