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 <iostream>
#include <algorithm>
typedef long long ll;
using namespace std;

ll A[200010], dp[200010][5]={};

int main(void){
    int L;
    cin >> L;
    for(int i=0; i<L; ++i) cin >> A[i];
    for(int i=0; i<L; ++i){
        ll mn=1e18;
        for(int j=0; j<5; ++j){
            mn=min(mn, dp[i][j]);
            if(j==0 || j==4) dp[i+1][j]=mn+A[i];
            else if(j==2) dp[i+1][j]=mn+(1-A[i]%2);
            else if(A[i]>0) dp[i+1][j]=mn+A[i]%2;
            else dp[i+1][j]=mn+2;
        }
    }
    ll ans=1e18;
    for(int i=0; i<5; ++i) ans=min(ans, dp[L][i]);
    cout << ans << endl;
    return 0;
}
