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

int main()
{
	ll n, a[200010];
	cin >> n;
	rep(i, n)
	{
		cin >> a[i];
	}
	ll sum[200010];
	sum[0]=0;
	rep(i, n) sum[i+1]=sum[i]+a[i];
	rep(i, n)
	{
		if(a[i]%2==0 && a[i]>=2) a[i]=2;
		else a[i]%=2;
	}
	ll le[200010], re[200010];
	le[0]=0; re[n]=0;
	rep(i, n)
	{
		le[i+1]=min((2-a[i])+le[i], sum[i+1]);
		re[n-(i+1)]=min((2-a[n-(i+1)])+re[n-i], sum[n]-sum[n-(i+1)]);
	}
	ll dp[200010];
	dp[0]=0;
	rep(i, n)
	{
		if(a[i]<2)
		{
			dp[i+1]=min((1-a[i])+dp[i], le[i+1]);
		}
		else
		{
			dp[i+1]=min(dp[i]+1, le[i+1]);
		}
	}
	ll ans=2*n;
	rep(i, n+1) ans=min(ans, dp[i]+re[i]);
	cout << ans << endl;
	return 0;
}