#include <bits/stdc++.h>

using namespace std;

int n;
long long dp[200002][5];

int c1(int a){
    if(a%2) return 0;
    else return 1;
}
int c2(int a){
    if(a == 0) return 2;
    else if(a%2) return 1;
    else return 0;
}
void solve(){
    int i;
    long long j;
    string str;
    cin >> n;
    vector<int> a(n);
    for(i = 0;i < n;i++) cin >> a[i];
    a.push_back(0);
    for(i = 0;i < a.size();i++){
        dp[i+1][0] = dp[i][0]+a[i];
        j = min(dp[i][0],dp[i][1]);
        dp[i+1][1] = j+c2(a[i]);
        j = min(j,dp[i][2]);
        dp[i+1][2] = j+c1(a[i]);
        j = min(j,dp[i][3]);
        dp[i+1][3] = j+c2(a[i]);
        j = min(j,dp[i][4]);
        dp[i+1][4] = j+a[i];
    }
    long long ans = 0;
    cout << dp[n+1][4] << endl;
}

int main(){
    solve();
}

### Prompt

Develop a solution in Cpp to the problem described below:

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;

int n;
long long dp[200002][5];

int c1(int a){
    if(a%2) return 0;
    else return 1;
}
int c2(int a){
    if(a == 0) return 2;
    else if(a%2) return 1;
    else return 0;
}
void solve(){
    int i;
    long long j;
    string str;
    cin >> n;
    vector<int> a(n);
    for(i = 0;i < n;i++) cin >> a[i];
    a.push_back(0);
    for(i = 0;i < a.size();i++){
        dp[i+1][0] = dp[i][0]+a[i];
        j = min(dp[i][0],dp[i][1]);
        dp[i+1][1] = j+c2(a[i]);
        j = min(j,dp[i][2]);
        dp[i+1][2] = j+c1(a[i]);
        j = min(j,dp[i][3]);
        dp[i+1][3] = j+c2(a[i]);
        j = min(j,dp[i][4]);
        dp[i+1][4] = j+a[i];
    }
    long long ans = 0;
    cout << dp[n+1][4] << endl;
}

int main(){
    solve();
}

```