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

int main(){
    int L;
    cin >> L;
    vector<ll> a(L+1, 0);
    for (int i = 1; i <= L; i++) cin >> a[i];
    
    vector<vector<ll>> dp(L+1, vector<ll>(5, 0));
    for (int i = 1; i <= L; i++) {
        ll t = dp[i-1][0];
        dp[i][0] = t+a[i];
        t = min(t, dp[i-1][1]);
        dp[i][1] = t + ((a[i] == 0) ? 2 : a[i]%2);
        t = min(t, dp[i-1][2]);
        dp[i][2] = t + (a[i]+1)%2;
        t = min(t, dp[i-1][3]);
        dp[i][3] = t + ((a[i] == 0) ? 2 : a[i]%2);
        t = min(t, dp[i-1][4]);
        dp[i][4] = t + a[i];
    }
    
    ll ans = dp[L][0];
    for (int i = 1; i <= 4; i++) ans = min(ans, dp[L][i]);
    cout << ans << endl;
    return 0;
}

### 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 ll long long

int main(){
    int L;
    cin >> L;
    vector<ll> a(L+1, 0);
    for (int i = 1; i <= L; i++) cin >> a[i];
    
    vector<vector<ll>> dp(L+1, vector<ll>(5, 0));
    for (int i = 1; i <= L; i++) {
        ll t = dp[i-1][0];
        dp[i][0] = t+a[i];
        t = min(t, dp[i-1][1]);
        dp[i][1] = t + ((a[i] == 0) ? 2 : a[i]%2);
        t = min(t, dp[i-1][2]);
        dp[i][2] = t + (a[i]+1)%2;
        t = min(t, dp[i-1][3]);
        dp[i][3] = t + ((a[i] == 0) ? 2 : a[i]%2);
        t = min(t, dp[i-1][4]);
        dp[i][4] = t + a[i];
    }
    
    ll ans = dp[L][0];
    for (int i = 1; i <= 4; i++) ans = min(ans, dp[L][i]);
    cout << ans << endl;
    return 0;
}

```