#include<bits/stdc++.h>
#define N 500005
using namespace std;
typedef long long LL;
LL sum[N],pre[N],succ[N],dp[N];
int even[N],n,a[N];
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
		scanf("%d",&a[i]),sum[i]=sum[i-1]+a[i];
	for (int i=1;i<=n;i++){
		pre[i]=sum[i];
		pre[i]=min(pre[i],pre[i-1]+(a[i]<2?2-a[i]:(a[i]&1)));
	}
	for (int i=n-1;i>=0;i--){
		succ[i]=sum[n]-sum[i];
		succ[i]=min(succ[i],succ[i+1]+(a[i+1]<2?2-a[i+1]:(a[i+1]&1)));
	}
	for (int i=1;i<=n;i++)
		even[i]=even[i-1]+(a[i]&1^1);
	dp[n]=even[n]+succ[n];
	for (int i=n-1;i>=0;i--)
		dp[i]=min(dp[i+1],even[i]+succ[i]);
	LL ans=1e18;
	for (int i=0;i<=n;i++)
		ans=min(ans,pre[i]+dp[i]-even[i]);
	printf("%lld\n",ans);
}
### Prompt

Generate a Cpp solution to the following problem:

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

### Response

```cpp
#include<bits/stdc++.h>
#define N 500005
using namespace std;
typedef long long LL;
LL sum[N],pre[N],succ[N],dp[N];
int even[N],n,a[N];
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
		scanf("%d",&a[i]),sum[i]=sum[i-1]+a[i];
	for (int i=1;i<=n;i++){
		pre[i]=sum[i];
		pre[i]=min(pre[i],pre[i-1]+(a[i]<2?2-a[i]:(a[i]&1)));
	}
	for (int i=n-1;i>=0;i--){
		succ[i]=sum[n]-sum[i];
		succ[i]=min(succ[i],succ[i+1]+(a[i+1]<2?2-a[i+1]:(a[i+1]&1)));
	}
	for (int i=1;i<=n;i++)
		even[i]=even[i-1]+(a[i]&1^1);
	dp[n]=even[n]+succ[n];
	for (int i=n-1;i>=0;i--)
		dp[i]=min(dp[i+1],even[i]+succ[i]);
	LL ans=1e18;
	for (int i=0;i<=n;i++)
		ans=min(ans,pre[i]+dp[i]-even[i]);
	printf("%lld\n",ans);
}
```