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

#define rep(i, N) for (int i = 0; i < (N); i++)
#define all(a) (a).begin(), (a).end()
#define pb push_back

using ll = long long;
using i_i = tuple<int, int>;

int main() {
    int N; cin >> N;
    vector<ll> a(N);
    rep(i, N) cin >> a[i];
    vector<ll> dp(5);
    rep(i, N) {
        dp[0] += a[i];
        
        if (a[i] == 0) dp[1] += 2;
        else dp[1] += a[i] % 2;
        
        dp[2] += (a[i] + 1) % 2;
        
        if (a[i] == 0) dp[3] += 2;
        else dp[3] += a[i] % 2;
        
        dp[4] += a[i];
        
        rep(k, 4) dp[k + 1] = min(dp[k + 1], dp[k]);
    }
    cout << dp[4] << 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 rep(i, N) for (int i = 0; i < (N); i++)
#define all(a) (a).begin(), (a).end()
#define pb push_back

using ll = long long;
using i_i = tuple<int, int>;

int main() {
    int N; cin >> N;
    vector<ll> a(N);
    rep(i, N) cin >> a[i];
    vector<ll> dp(5);
    rep(i, N) {
        dp[0] += a[i];
        
        if (a[i] == 0) dp[1] += 2;
        else dp[1] += a[i] % 2;
        
        dp[2] += (a[i] + 1) % 2;
        
        if (a[i] == 0) dp[3] += 2;
        else dp[3] += a[i] % 2;
        
        dp[4] += a[i];
        
        rep(k, 4) dp[k + 1] = min(dp[k + 1], dp[k]);
    }
    cout << dp[4] << endl;
}

```