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;

const long long inf = 1e16;

int main(){
  long long L; cin >> L;
  vector<long long> A(L);
  for (int i=0; i<L; i++) cin >> A[i];
  vector<vector<long long>> dp(L+1, vector<long long>(5,inf));
  for (int i=0; i<5; i++) dp[0][i] = 0;
  for (int l=1; l<=L; l++){
    dp[l][0] = dp[l-1][0] + A[l-1];
    dp[l][1] = min(dp[l][0], dp[l-1][1] + ((A[l-1]==0)? 2:A[l-1]%2));
    dp[l][2] = min(dp[l][1], dp[l-1][2] + (A[l-1]+1)%2);
    dp[l][3] = min(dp[l][2], dp[l-1][3] + ((A[l-1]==0)? 2:A[l-1]%2));
    dp[l][4] = min(dp[l][3], dp[l-1][4] + A[l-1]);
  }
  cout << dp[L][4] << endl;
}
