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 <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
#define ll long long
#define Maxn 200000
int a[Maxn+5];
ll sum[Maxn+5];
ll f[Maxn+5],g[Maxn+5],d[Maxn+5];
int main(){
	int n;
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		scanf("%d",&a[i]);
	}
	for(int i=0;i<n;i++){
		sum[i+1]=sum[i]+a[i];
	}
	for(int i=0;i<n;i++){
		f[i+1]=min(sum[i+1],f[i]+(a[i]==0?2:(a[i]&1)));
		g[n-i-1]=min(sum[n]-sum[n-i-1],g[n-i]+(a[n-i-1]==0?2:(a[n-i-1]&1)));
		d[i+1]=d[i]+(a[i]&1)-1;
	}
	g[n]-=d[n];
	for(int i=0;i<n;i++){
		f[i]+=d[i];
		g[n-i-1]-=d[n-i-1];
		g[n-i-1]=min(g[n-i-1],g[n-i]);
	}
	ll ans=f[0]+g[0];
	for(int i=1;i<=n;i++){
		ans=min(ans,f[i]+g[i]);
	}
	cout<<ans<<endl;
	return 0;
}
