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;
#define N 200100
#define ll long long

int n;
int a[N];
ll dp[N][10],ans;

int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	memset(dp[0],0x3f,sizeof(dp[0]));
	dp[0][1]=0;
	for (int i=1;i<=n;i++) {
		ll now=dp[i-1][1];
		for (int j=1;j<=5;j++) {
			now=min(now,dp[i-1][j]);
			if (j==1 || j==5) dp[i][j]=now+a[i];
			if (j==2 || j==4) dp[i][j]=now+(a[i]==0 ? 2 : a[i]&1);
			if (j==3) dp[i][j]=now+(a[i]&1^1);
		}
	}
	ans=dp[0][0];
	for (int i=1;i<=5;i++) ans=min(ans,dp[n][i]);
	printf("%lld\n",ans);
	return 0;
}