#include <iostream>
#include <algorithm>
using namespace std;

int a[200005];
int dp[200005][5];

int main() {
  int l;
  cin >> l;
  for(int i = 0; i < l; i++) cin >> a[i];

  for(int i = 0; i <= l; i++) {
    for(int j = 0; j < 5; j++) {
      dp[i][j] = 1e9;
    }
  }
  dp[0][0] = 0;

  for(int i = 1; i <= l; i++) {
      int pre = 1e9;
      for(int k = 0; k < 5; k++) {
	pre = min(pre,dp[i-1][k]);
	int tmp;
	if(k == 0 || k == 4) tmp = a[i-1];
	if(k == 1 || k == 3) tmp = (a[i-1] == 0 ? 2 : a[i-1] % 2);
	if(k == 2) tmp = (a[i-1]+1) % 2;
	dp[i][k] = pre + tmp;
      }
    
  }

  int ans = 1e9;

  for(int i = 0; i < 5; i++) ans = min(ans,dp[l][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 <iostream>
#include <algorithm>
using namespace std;

int a[200005];
int dp[200005][5];

int main() {
  int l;
  cin >> l;
  for(int i = 0; i < l; i++) cin >> a[i];

  for(int i = 0; i <= l; i++) {
    for(int j = 0; j < 5; j++) {
      dp[i][j] = 1e9;
    }
  }
  dp[0][0] = 0;

  for(int i = 1; i <= l; i++) {
      int pre = 1e9;
      for(int k = 0; k < 5; k++) {
	pre = min(pre,dp[i-1][k]);
	int tmp;
	if(k == 0 || k == 4) tmp = a[i-1];
	if(k == 1 || k == 3) tmp = (a[i-1] == 0 ? 2 : a[i-1] % 2);
	if(k == 2) tmp = (a[i-1]+1) % 2;
	dp[i][k] = pre + tmp;
      }
    
  }

  int ans = 1e9;

  for(int i = 0; i < 5; i++) ans = min(ans,dp[l][i]);

  cout << ans << endl;
}

  
  

```