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,n)for(int i=0;i<(n);i++)
#define INF 0x3f3f3f3f3f3f3f3f
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

ll dp[300000][5];
int a[300000];

int main(){
	int n;scanf("%d",&n);
	rep(i,n)scanf("%d",&a[i]);
	memset(dp,0x3f,sizeof(dp));
	dp[0][0]=0;
	rep(i,n){
		dp[i+1][0]=dp[i][0]+a[i];
		dp[i+1][1]=min(dp[i][0],dp[i][1])+(a[i]?a[i]%2:2);
		dp[i+1][2]=min({dp[i][0],dp[i][1],dp[i][2]})+(a[i]?!(a[i]%2):1);
		dp[i+1][3]=min({dp[i][0],dp[i][1],dp[i][2],dp[i][3]})+(a[i]?a[i]%2:2);
		dp[i+1][4]=min({dp[i][0],dp[i][1],dp[i][2],dp[i][3],dp[i][4]})+a[i];
	}
	ll Min=INF;
	rep(i,5)Min=min(Min,dp[n][i]);
	cout<<Min<<endl;
}