#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll dp[200005][5]={0};
ll ear[200005]={0};
const ll inf=17441744174417;
int main(){
  ll n;
  cin>>n;
  for(int i=1;i<=n;i++) cin>>ear[i];
  for(int i=1;i<=n;i++){
    for(int j=0;j<5;j++) dp[i][j]=inf;
  }
  for(int i=1;i<=n;i++){
    for(int j=0;j<5;j++){
      for(int k=0;k<=j;k++) dp[i][j]=min(dp[i][j],dp[i-1][k]);
      if(j==0||j==4) dp[i][j]+=ear[i];
      else if(j==1||j==3){
        if(ear[i]<2) dp[i][j]+=2-ear[i];
        else if(ear[i]%2==1) dp[i][j]++;
      }
      else{
        if(ear[i]%2==0) dp[i][j]++;
      }
    }
  }
  ll ans=inf;
  for(int i=0;i<5;i++) ans=min(ans,dp[n][i]);
  cout<<ans<<endl;
}

### Prompt

Create a solution in cpp for 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;
typedef long long ll;
ll dp[200005][5]={0};
ll ear[200005]={0};
const ll inf=17441744174417;
int main(){
  ll n;
  cin>>n;
  for(int i=1;i<=n;i++) cin>>ear[i];
  for(int i=1;i<=n;i++){
    for(int j=0;j<5;j++) dp[i][j]=inf;
  }
  for(int i=1;i<=n;i++){
    for(int j=0;j<5;j++){
      for(int k=0;k<=j;k++) dp[i][j]=min(dp[i][j],dp[i-1][k]);
      if(j==0||j==4) dp[i][j]+=ear[i];
      else if(j==1||j==3){
        if(ear[i]<2) dp[i][j]+=2-ear[i];
        else if(ear[i]%2==1) dp[i][j]++;
      }
      else{
        if(ear[i]%2==0) dp[i][j]++;
      }
    }
  }
  ll ans=inf;
  for(int i=0;i<5;i++) ans=min(ans,dp[n][i]);
  cout<<ans<<endl;
}

```