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;
int n;
int a[200005] ;
long long f[200005][5] ;
int main()
{
    scanf("%d",&n) ;
    int ans = 0;
    for(int i = 1;i <= n;i++){
        scanf("%d",&a[i]) ;
    }
    for(int i = 1;i <= n;i++) {
        f[i][0] = f[i - 1][0] + a[i] ;
        f[i][1] = min(f[i - 1][0] , f[i - 1][1]) + (a[i] % 2 == 1) ;
        f[i][2] = min(f[i - 1][1] , min(f[i-1][0],f[i - 1][2])) + (a[i] % 2 == 0) ;
        f[i][3] = min(f[i - 1][2] , f[i - 1][3]) + (a[i] % 2 == 1) ;
        f[i][4] = min(f[i - 1][3] , min(f[i - 1][1] , min(f[i-1][2] , f[i - 1][4]))) + a[i] ;
        if(a[i] == 0) {f[i][1]+=2 ; f[i][3]+=2 ;}
    }
    printf("%lld\n",min(f[n][0] , min(f[n][1] , min(f[n][2] , min(f[n][3] , f[n][4])))));
    return 0;
}
