#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;

Int dp[216000][5], a, l;

int main(){
  cin >> l;
  for(int i = 0;i < l;i++)
    for(int j = 0;j < 5;j++)
      dp[i][j] = INF;
  dp[0][0] = dp[0][1] = dp[0][2] = dp[0][3] = dp[0][4] = 0;
  for(int i = 1;i <= l;i++){
    cin >> a;
    dp[i][0] = dp[i-1][0] + a;
    dp[i][1] = min(dp[i][0], dp[i-1][1] + (a==0?2:(a%2)));
    dp[i][2] = min(dp[i][1], dp[i-1][2] + !(a%2));
    dp[i][3] = min(dp[i][2], dp[i-1][3]  +(a==0?2:(a%2)));
    dp[i][4] = min(dp[i][3], dp[i-1][4] + a);
  }
  cout << dp[l][4] << endl;
  return 0;
}

### Prompt

Please provide a CPP coded solution 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<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;

Int dp[216000][5], a, l;

int main(){
  cin >> l;
  for(int i = 0;i < l;i++)
    for(int j = 0;j < 5;j++)
      dp[i][j] = INF;
  dp[0][0] = dp[0][1] = dp[0][2] = dp[0][3] = dp[0][4] = 0;
  for(int i = 1;i <= l;i++){
    cin >> a;
    dp[i][0] = dp[i-1][0] + a;
    dp[i][1] = min(dp[i][0], dp[i-1][1] + (a==0?2:(a%2)));
    dp[i][2] = min(dp[i][1], dp[i-1][2] + !(a%2));
    dp[i][3] = min(dp[i][2], dp[i-1][3]  +(a==0?2:(a%2)));
    dp[i][4] = min(dp[i][3], dp[i-1][4] + a);
  }
  cout << dp[l][4] << endl;
  return 0;
}

```