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 <stdio.h>
#include <algorithm>
using namespace std;
using ll = long long;

int n, a[200100];
ll dp[200100][5];
int f(int x) {
	return x;
}
int g(int x) {
	return (x & 1) ^ 1;
}
int h(int x) {
	if (x == 0)
		return 2;
	return x & 1;
}
int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) {
		scanf("%d", a + i);
		ll p = dp[i - 1][0];
		dp[i][0] = p + f(a[i]);
		p = min(p, dp[i - 1][1]);
		dp[i][1] = p + h(a[i]);
		p = min(p, dp[i - 1][2]);
		dp[i][2] = p + g(a[i]);
		p = min(p, dp[i - 1][3]);
		dp[i][3] = p + h(a[i]);
		p = min(p, dp[i - 1][4]);
		dp[i][4] = p + f(a[i]);
	}
	ll min_c = 2e18;
	for (int i = 0; i < 5; i++)
		min_c = min(dp[n][i], min_c);
	printf("%lld\n", min_c);
}