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;
#define int long long
    



signed main(){
    int l,t;
    cin >> l;
    int a[l][5],u[4];
    cin >> t;
    a[0][0]=t;
    a[0][1]=( t==0 ? 2 : t%2);
    a[0][2]=(t+1)%2;
    a[0][3]=( t==0 ? 2 : t%2);
    a[0][4]=t;
    for(int i=1;i<l;i++){
        cin >> t;
        a[i][0]=a[i-1][0]+t;
        u[0]=min(a[i-1][0],a[i-1][1]);u[1]=min(u[0],a[i-1][2]);u[2]=min(u[1],a[i-1][3]);u[3]=min(u[2],a[i-1][4]);
        a[i][1]=u[0]+( t==0 ? 2 : t%2);a[i][2]=u[1]+((t+1)%2);a[i][3]=u[2]+( t==0 ? 2 : t%2);a[i][4]=u[3]+t;
    }
    int ans=a[l-1][0];
    
    for(int i=1;i<5;i++)if(ans>a[l-1][i])ans=a[l-1][i];
    cout << ans;
    return 0;
}