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;

int a[200010];
long long dp[200010][5];

int main(){
	int n;
	scanf("%d", &n);
	for (int i = 1; i <= n; i++){
		scanf("%d", &a[i]);
	}
	for (int i = 1; i <= n; i++){
		dp[i][0] = dp[i - 1][0] + a[i];
	}
	for (int i = 1; i <= n; i++){
		dp[i][1] = min(dp[i - 1][1] + (!a[i] ? 2 : a[i] % 2 == 1), dp[i][0]);
	}
	for (int i = 1; i <= n; i++){
		dp[i][2] = min(dp[i - 1][2] + (!a[i] ? 1 : a[i] % 2 == 0), dp[i][1]);
	}
	for (int i = 1; i <= n; i++){
		dp[i][3] = min(dp[i - 1][3] + (!a[i] ? 2 : a[i] % 2 == 1), dp[i][2]);
	}
	for (int i = 1; i <= n; i++){
		dp[i][4] = min(dp[i - 1][4] + a[i], dp[i][3]);
	}
	printf("%lld\n", dp[n][4]);
	return 0;
}
