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;

const int N = 200005, INF = int(1e9);

int n, a[N], d[N][5];

int c(int x, int y){
    if(y == 2) return (a[x] % 2 == 0);
    if(y == 1 || y == 3) return 2 * !a[x] + (a[x] % 2);
    return a[x];
}

int main(){
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) scanf("%d", a + i);
    for(int i = 1; i <= n; i++){
        int t = INF;
        for(int j = 0; j < 5; j++){
            t = min(t, d[i - 1][j]);
            d[i][j] = t + c(i, j);
        }
    }
    printf("%d\n", *min_element(d[n], d[n] + 5));
}