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 rep(i,n) for(ll i=0;i<n;i++)
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vec;
typedef vector<vec> mat;
ll L,A[200001],B[200001][5],dp[200001][5],inf=1e18;
int main(){
    cin>>L;
    rep(i,L) cin>>A[i];
    rep(i,L){
        B[i][0]=A[i];
        B[i][4]=A[i];
        if(A[i]==0) B[i][1]=2;
        else B[i][1]=A[i]%2;
        B[i][3]=B[i][1];
        B[i][2]=(A[i]+1)%2;
    }
    rep(i,L)rep(j,5) dp[i][j]=inf;
    rep(i,5) dp[L][i]=0;
    for(int i=L-1;i>=0;i--)rep(j,5)rep(k,j+1) dp[i][j]=min(dp[i][j],dp[i+1][k]+B[i][j]);
    cout<<min({dp[0][0],dp[0][1],dp[0][2],dp[0][3],dp[0][4]})<<"\n";
}