#include <bits/stdc++.h>

using namespace std;

using ll = long long;

const ll INF = 1e18;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<ll> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }

    vector< vector<ll> > dp(n + 1, vector<ll>(5, INF));
    dp[0][0] = 0;
    for (int i = 0; i < n; i++) {
        dp[i+1][0] = dp[i][0] + a[i];
        dp[i+1][1] = *min_element(dp[i].begin(), dp[i].begin() + 2) + (a[i] == 0 ? 2 : a[i] % 2);
        dp[i+1][2] = *min_element(dp[i].begin(), dp[i].begin() + 3) + 1 - a[i] % 2;
        dp[i+1][3] = *min_element(dp[i].begin(), dp[i].begin() + 4) + (a[i] == 0 ? 2 : a[i] % 2);
        dp[i+1][4] = *min_element(dp[i].begin(), dp[i].begin() + 5) + a[i];
    }
    cout << *min_element(dp[n].begin(), dp[n].end()) << endl;
    return 0;
}
### Prompt

Your challenge is to write 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;

using ll = long long;

const ll INF = 1e18;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<ll> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }

    vector< vector<ll> > dp(n + 1, vector<ll>(5, INF));
    dp[0][0] = 0;
    for (int i = 0; i < n; i++) {
        dp[i+1][0] = dp[i][0] + a[i];
        dp[i+1][1] = *min_element(dp[i].begin(), dp[i].begin() + 2) + (a[i] == 0 ? 2 : a[i] % 2);
        dp[i+1][2] = *min_element(dp[i].begin(), dp[i].begin() + 3) + 1 - a[i] % 2;
        dp[i+1][3] = *min_element(dp[i].begin(), dp[i].begin() + 4) + (a[i] == 0 ? 2 : a[i] % 2);
        dp[i+1][4] = *min_element(dp[i].begin(), dp[i].begin() + 5) + a[i];
    }
    cout << *min_element(dp[n].begin(), dp[n].end()) << endl;
    return 0;
}
```