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 ll long long
#define inf 1e18

int main(){
    int L;  cin >> L;
    vector<ll> a(L+1,0);
    for(int i=1; i<=L; i++) cin >> a[i];

    vector<vector<ll>> dp;
    dp = vector<vector<ll>>(L+2, vector<ll>(5,0));
    for(int i=1; i<=L; i++){
        ll prev = inf;
        for(int t=0; t<=4; t++){
            prev = min(prev, dp[i-1][t]);
            if(t==0 || t==4) dp[i][t] = prev + a[i];
            if(t==1 || t==3) dp[i][t] = prev + (a[i]==0 ? 2:a[i]%2);
            if(t==2) dp[i][t] = prev + 1 - a[i]%2;
        }
    }

    ll ans = inf;
    for(int t=0; t<=4; t++) ans = min(ans, dp[L][t]);
    cout << ans << endl;
}
