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;
typedef long long ll;
typedef long double ld;
typedef double db;// при желании можно поменять
ll a[300000];
ll s0,s1,s2,s3,s4;
int main(){
    //ios_base::sync_with_stdio(false);
    //cout<<fixed<<setprecision(20);
    int n;
    cin>>n;
    for(int i=0;i<n;i++){
        ll a;
        cin>>a;
        ll x0,x1,x2,x3,x4;
        x0=s0+a;
        ll delt=0;
        if(a==0)delt=2;
        if(a%2==1)delt=1;
        x1=min(x0,s1+delt);
        ll c=0;
        if(a%2==0)c=1;
        x2=min(x1,s2+c);
        x3=min(x2,s3+delt);
        x4=min(x3,s4+a);
        s0=x0;
        s1=x1;
        s2=x2;
        s3=x3;
        s4=x4;
    }
    cout<<s4;
    return 0;
}