#include <bits/stdc++.h>

using namespace std;

const int INF = 1 << 30;

int L, X[200000];
int dp[200002][5];

int rec(int idx, int state) {
  if(idx == L) return 0;
  if(~dp[idx][state]) return dp[idx][state];
  int ret = INF;
  if(state == 0 || state == 4) {
    ret = min(ret, rec(idx + 1, state) + X[idx]);
    if(state == 0) ret = min(ret, rec(idx, state + 1));
  } else if(state == 1 || state == 3) {
    ret = min(ret, rec(idx + 1, state) + (X[idx] == 0 ? 2 : X[idx] % 2));
    ret = min(ret, rec(idx, state + 1));
  } else {
    ret = min(ret, rec(idx + 1, state) + 1 - X[idx] % 2);
    ret = min(ret, rec(idx, state + 1));
  }
  return dp[idx][state] = ret;
}

int main() {
  cin >> L;
  for(int i = 0; i < L; i++) cin >> X[i];
  memset(dp, -1, sizeof(dp));
  cout << rec(0, 0) << endl;
}

### Prompt

Please create a solution in cpp 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;

const int INF = 1 << 30;

int L, X[200000];
int dp[200002][5];

int rec(int idx, int state) {
  if(idx == L) return 0;
  if(~dp[idx][state]) return dp[idx][state];
  int ret = INF;
  if(state == 0 || state == 4) {
    ret = min(ret, rec(idx + 1, state) + X[idx]);
    if(state == 0) ret = min(ret, rec(idx, state + 1));
  } else if(state == 1 || state == 3) {
    ret = min(ret, rec(idx + 1, state) + (X[idx] == 0 ? 2 : X[idx] % 2));
    ret = min(ret, rec(idx, state + 1));
  } else {
    ret = min(ret, rec(idx + 1, state) + 1 - X[idx] % 2);
    ret = min(ret, rec(idx, state + 1));
  }
  return dp[idx][state] = ret;
}

int main() {
  cin >> L;
  for(int i = 0; i < L; i++) cin >> X[i];
  memset(dp, -1, sizeof(dp));
  cout << rec(0, 0) << endl;
}

```