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<iostream>
#include<cstdio>
#define int long long

using namespace std;

int n,a[200005],s[200005],sum[200005],t[200005],v[200005];

int kk1(int o) 
{
	if(o==0) return 2;
	return o%2!=0;
}

signed main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;i++) 
	{
		scanf("%lld",&a[i]);
		sum[i]=sum[i-1]+a[i];
	}
	for(int i=1;i<=n;i++)
		s[i]=min(s[i-1]+kk1(a[i]),sum[i]);
	for(int i=1;i<=n;i++)
		t[i]=min(t[i-1]+(a[i]%2==0),s[i]);
	for(int i=n-1;i>=1;i--)
		v[i]=min(v[i+1]+kk1(a[i+1]),sum[n]-sum[i]);
	int ans=1e17;
	for(int i=1;i<=n;i++) ans=min(ans,t[i]+v[i]);
	cout<<ans<<endl;
	return 0;
}