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;
#define N 200010
ll a[N],b[N],c[N],d[N],e[N],f[N],n;
int main(){
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>a[i];
    b[i]=c[i]=d[i]=e[i]=f[i]=1e17;
  }
  b[0]=0;
  for(int i=0;i<n;i++){
    ll xs,ys;
    if(a[i]==0)xs=2,ys=1;
    else if(a[i]%2==1)xs=1,ys=0;
    else xs=0,ys=1;
    b[i+1]=b[i]+a[i];
    c[i+1]=min(b[i],c[i])+xs;
    d[i+1]=min(min(b[i],c[i]),d[i])+ys;
    e[i+1]=min(d[i],e[i])+xs;
    f[i+1]=min(min(c[i],d[i]),min(e[i],f[i]))+a[i];
  }
  ll ans=min(min(b[n],c[n]),min(min(d[n],e[n]),f[n]));
  cout<<ans<<endl;
  return 0;
}
