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 long a[200005],dp[5][200005];
int main()
{
	long long n,i;
	cin>>n;
	for(i=1;i<=n;i++)
		cin>>a[i];
	for(i=1;i<=n;i++)
	{
		dp[0][i]=dp[0][i-1]+a[i];
		dp[1][i]=min(dp[0][i-1],dp[1][i-1])+a[i]%2+2*(a[i]==0);
		dp[2][i]=min(dp[0][i-1],min(dp[1][i-1],dp[2][i-1]))+(a[i]+1)%2;
		dp[3][i]=min(dp[0][i-1],min(dp[1][i-1],min(dp[2][i-1],dp[3][i-1])))+a[i]%2+2*(a[i]==0);
		dp[4][i]=min(dp[0][i-1],min(dp[1][i-1],min(dp[2][i-1],min(dp[3][i-1],dp[4][i-1]))))+a[i];
	}
	cout<<min(dp[0][i-1],min(dp[1][i-1],min(dp[2][i-1],min(dp[3][i-1],dp[4][i-1]))))<<'\n';
}
