#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define M 1000000000000000000
int main(){
  int n;
  cin>>n;
  vector<int> a(n);
  for(int i=0;i<n;i++) cin>>a[i];
  vector<vector<ll>> dp(n,vector<ll>(5));
  dp[0][0]=dp[0][4]=a[0];
  dp[0][1]=dp[0][3]=(a[0]==0?2:a[0]%2==0?0:1);
  dp[0][2]=(a[0]%2==0?1:0);
  for(int i=1;i<n;i++){
    dp[i][0]=dp[i-1][0]+a[i];
    dp[i][1]=min(dp[i-1][0],dp[i-1][1])+(a[i]==0?2:a[i]%2==0?0:1);
    dp[i][2]=min({dp[i-1][0],dp[i-1][1],dp[i-1][2]})+(a[i]%2==0?1:0);
    dp[i][3]=min({dp[i-1][0],dp[i-1][1],dp[i-1][2],dp[i-1][3]})+(a[i]==0?2:a[i]%2==0?0:1);
    dp[i][4]=min({dp[i-1][0],dp[i-1][1],dp[i-1][2],dp[i-1][3],dp[i-1][4]})+a[i];
  }
  cout<<min({dp[n-1][0],dp[n-1][1],dp[n-1][2],dp[n-1][3],dp[n-1][4]});
}
### 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
#define M 1000000000000000000
int main(){
  int n;
  cin>>n;
  vector<int> a(n);
  for(int i=0;i<n;i++) cin>>a[i];
  vector<vector<ll>> dp(n,vector<ll>(5));
  dp[0][0]=dp[0][4]=a[0];
  dp[0][1]=dp[0][3]=(a[0]==0?2:a[0]%2==0?0:1);
  dp[0][2]=(a[0]%2==0?1:0);
  for(int i=1;i<n;i++){
    dp[i][0]=dp[i-1][0]+a[i];
    dp[i][1]=min(dp[i-1][0],dp[i-1][1])+(a[i]==0?2:a[i]%2==0?0:1);
    dp[i][2]=min({dp[i-1][0],dp[i-1][1],dp[i-1][2]})+(a[i]%2==0?1:0);
    dp[i][3]=min({dp[i-1][0],dp[i-1][1],dp[i-1][2],dp[i-1][3]})+(a[i]==0?2:a[i]%2==0?0:1);
    dp[i][4]=min({dp[i-1][0],dp[i-1][1],dp[i-1][2],dp[i-1][3],dp[i-1][4]})+a[i];
  }
  cout<<min({dp[n-1][0],dp[n-1][1],dp[n-1][2],dp[n-1][3],dp[n-1][4]});
}
```