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
#include<bits/stdc++.h>
using namespace std;
int64_t dp[5][200010];
static const int64_t INF=1000000000000000;
int64_t L;
int64_t A[200010];
int main(){
  cin>>L;
  for(int i=0;i<L;i++)
    cin>>A[i];
  dp[0][0]=A[0];dp[4][0]=INF;
  dp[1][0]=max(A[0]%2,2-A[0]);dp[3][0]=INF;
  dp[2][0]=(A[0]+1)%2;
  for(int j=1;j<L;j++){
dp[0][j]=dp[0][j-1]+A[j];
    dp[1][j]=min(dp[0][j-1],dp[1][j-1])+max(A[j]%2,2-A[j]);
    dp[2][j]=min(dp[2][j-1],min(dp[0][j-1],dp[1][j-1]))+(A[j]+1)%2;
    dp[3][j]=min(dp[2][j-1],dp[3][j-1])+max(A[j]%2,2-A[j]);
    dp[4][j]=min(dp[1][j-1],min(dp[4][j-1],min(dp[2][j-1],dp[3][j-1])))+A[j];
  }int64_t ans=INF;
  for(int i=0;i<5;i++)
    if(dp[i][L-1]<ans)
      ans=dp[i][L-1];
  cout<<ans<<endl;
  return 0;
}
