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;

long d[222222][5];
int main() {
	int l;
	cin >> l;
	for (int i = 0; i < l; i++) {
		int a;
		scanf("%d", &a);
		d[i + 1][0] = d[i][0] + a;
		d[i + 1][1] = min(d[i][0], d[i][1]) + a % 2 + !a * 2;
		d[i + 1][2] = min({ d[i][0],d[i][1],d[i][2] }) + 1 - a % 2;
		d[i + 1][3] = min({ d[i][0],d[i][1],d[i][2],d[i][3] }) + a % 2 + !a * 2;
		d[i + 1][4] = min({ d[i][0],d[i][1],d[i][2],d[i][3],d[i][4] }) + a;
	}
	cout << min({ d[l][0],d[l][1],d[l][2],d[l][3],d[l][4] }) << endl;
	return 0;
}
