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>
#define rep(i,x,y) for (int i=(x);i<=(y);i++)
#define ll long long
using namespace std;
const int N=5e5+100;
int n,a[N]; ll Min,f[N],g[N],sum[N],sum0[N],sum1[N],ans;
int main(){
	scanf("%d",&n);
	rep (i,1,n){
		scanf("%d",&a[i]);
		sum[i]=sum[i-1]+a[i];
		sum1[i]=sum1[i-1]+(a[i]&1)+2*(a[i]==0);
		sum0[i]=sum0[i-1]+(!(a[i]&1));
	}
	f[0]=0; Min=0;
	rep (i,1,n){
		f[i]=min(sum[i],Min+sum1[i]);
		Min=min(Min,sum[i]-sum1[i]);
	}
	g[0]=0; Min=0;
	rep (i,1,n){
		g[i]=min(f[i],Min+sum0[i]);
		Min=min(Min,f[i]-sum0[i]);
	}
	f[0]=0; Min=0;
	rep (i,1,n){
		f[i]=min(g[i],Min+sum1[i]);
		Min=min(Min,g[i]-sum1[i]);
	}
	ans=f[n];
	rep (i,1,n-1) ans=min(ans,f[i]+sum[n]-sum[i]);
	printf("%lld\n",ans);
	return 0;
}