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 ll long long
#define INF 1e18
using namespace std;
template <typename T> void read(T &x){
	x=0;char c=getchar();int fh=1;
	while (!isdigit(c)){if (c=='-')fh=-1;c=getchar();}
	while (isdigit(c))x=x*10+c-'0',c=getchar();
	x*=fh;
}
ll n,x,dp[200010][5],a[200010];
int main(){
	read(n);
	for (int i=1;i<=n;i++) read(a[i]);
	for (int i=0;i<=n+1;i++)
		for (int j=0;j<=4;j++) dp[i][j]=INF;
	dp[0][0]=0;
	for (int i=1;i<=n+1;i++){
		for (int j=0;j<=4;j++){
			for (int k=0;k<=j;k++) dp[i][j]=min(dp[i][j],dp[i-1][k]);
			if (abs(j-2)<=1){
				if (a[i]%2==j%2) dp[i][j]++;
				if (a[i]==0&&j%2==1)dp[i][j]+=2;
			}else{
				dp[i][j]+=a[i];
			}
		}
	}
	cout<<dp[n+1][4]<<endl;
	return 0;
}