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 <iostream>
#include <algorithm>

using namespace std;

int main() {
    int l;
    cin >> l;
    long dp[l+1][5];
    fill(dp[0], dp[l+1], 0);
    for (int i=0; i<l; i++) {
        long a; cin >> a;
        long best = 1e18;
        for (int j=0; j<5; j++) {
            dp[i+1][j] = best = min(best, dp[i][j]);
            if (j == 0 || j == 4) dp[i+1][j] += a;
            else if (j == 2) dp[i+1][j] += (a+1) % 2;
            else dp[i+1][j] += a % 2 + (a == 0 ? 2 : 0);
        }
    }
    cout << min({dp[l][0], dp[l][1], dp[l][2], dp[l][3], dp[l][4]}) << '\n';
    return 0;
}