#include<bits/stdc++.h>
using namespace std;
#define FOR(i,N) for(i=0;i<N;i++)
#define N 5
#define INF 1e9
typedef long long ll;
ll L;

ll cost(ll num, int s){
  ll cost;
  if( s == 0 || s == 4){
    cost = num;
  }else if ( s == 1 || s == 3 ){
    if (num == 0) cost = 2;
    else if(num % 2 == 0) cost = 0;
    else cost = 1;
  }else{
    if(num % 2 == 0) cost = 1;
    else cost = 0;
  }
  return cost;
}

int main(void){
  cin >> L;
  int i,j,k;
  vector<ll> A(L);
  FOR(i,L) cin >> A[i];

  ll dp[L+1][N];

  FOR(i,L) FOR(j,N) dp[i+1][j] = INF;
  FOR(j,N) dp[0][j] = 0;


  FOR(i,L){
    FOR(j,N){
      for(k = j; k < N; k++){
        dp[i+1][k] = min(dp[i+1][k], dp[i][j] + cost(A[i],k));
      }
    }
  }

  ll res = INF;
  FOR(j,N) res = min(res,dp[L][j]);
  cout << res << endl;
  return 0;
}
### Prompt

In Cpp, your task is to solve 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 FOR(i,N) for(i=0;i<N;i++)
#define N 5
#define INF 1e9
typedef long long ll;
ll L;

ll cost(ll num, int s){
  ll cost;
  if( s == 0 || s == 4){
    cost = num;
  }else if ( s == 1 || s == 3 ){
    if (num == 0) cost = 2;
    else if(num % 2 == 0) cost = 0;
    else cost = 1;
  }else{
    if(num % 2 == 0) cost = 1;
    else cost = 0;
  }
  return cost;
}

int main(void){
  cin >> L;
  int i,j,k;
  vector<ll> A(L);
  FOR(i,L) cin >> A[i];

  ll dp[L+1][N];

  FOR(i,L) FOR(j,N) dp[i+1][j] = INF;
  FOR(j,N) dp[0][j] = 0;


  FOR(i,L){
    FOR(j,N){
      for(k = j; k < N; k++){
        dp[i+1][k] = min(dp[i+1][k], dp[i][j] + cost(A[i],k));
      }
    }
  }

  ll res = INF;
  FOR(j,N) res = min(res,dp[L][j]);
  cout << res << endl;
  return 0;
}
```