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 <cstdio>
#include <algorithm>

using namespace std;
typedef long long int ll;

int main(){
    int L;
    scanf("%d", &L);
    ll A[L];
    for(int i=0;i<L;i++)
        scanf("%lld", &A[i]);
    ll dp[L+1][5];
    for(int j=0;j<5;j++) dp[0][j] = 0;
    for(int i=1;i<L+1;i++){
        ll A_is_zero = 0;
        if (A[i-1] == 0) A_is_zero = 2;
        dp[i][0] = dp[i-1][0] + A[i-1];
        dp[i][1] = min(dp[i][0], dp[i-1][1] +  A[i-1]%2 + A_is_zero);
        dp[i][2] = min(dp[i][1], dp[i-1][2] + (A[i-1]+1)%2);
        dp[i][3] = min(dp[i][2], dp[i-1][3] +  A[i-1]%2 + A_is_zero);
        dp[i][4] = min(dp[i][3], dp[i-1][4] +  A[i-1]);
    }
    printf("%lld\n", dp[L][4]);
    return 0;
}
