#include<cstdio>
#include<iostream>
using namespace std;
typedef long long ll;
const ll INF_ll=4611686018427387903;
const int N=2e5+10;
int n,a[N];ll dp[N][5],ans;
int main(){
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)scanf("%d",&a[i]);
	for(register int i=1;i<=n;i++){
		dp[i][0]=dp[i-1][0]+a[i];
		dp[i][1]=min(dp[i-1][1],dp[i-1][0])+(a[i]? (a[i]&1):2);
		dp[i][2]=min(dp[i-1][2],min(dp[i-1][1],dp[i-1][0]))+((a[i]&1)^1);
		dp[i][3]=min(dp[i-1][3],min(dp[i-1][2],min(dp[i-1][1],dp[i-1][0])))+(a[i]? (a[i]&1):2);
		dp[i][4]=min(dp[i-1][4],min(dp[i-1][3],min(dp[i-1][2],min(dp[i-1][1],dp[i-1][0]))))+a[i];
	}
	ans=dp[n][0];
	for(register int i=1;i<5;i++)ans=min(ans,dp[n][i]);
	printf("%lld\n",ans);
	return 0;
}
### Prompt

In cpp, your task is to solve 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<cstdio>
#include<iostream>
using namespace std;
typedef long long ll;
const ll INF_ll=4611686018427387903;
const int N=2e5+10;
int n,a[N];ll dp[N][5],ans;
int main(){
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)scanf("%d",&a[i]);
	for(register int i=1;i<=n;i++){
		dp[i][0]=dp[i-1][0]+a[i];
		dp[i][1]=min(dp[i-1][1],dp[i-1][0])+(a[i]? (a[i]&1):2);
		dp[i][2]=min(dp[i-1][2],min(dp[i-1][1],dp[i-1][0]))+((a[i]&1)^1);
		dp[i][3]=min(dp[i-1][3],min(dp[i-1][2],min(dp[i-1][1],dp[i-1][0])))+(a[i]? (a[i]&1):2);
		dp[i][4]=min(dp[i-1][4],min(dp[i-1][3],min(dp[i-1][2],min(dp[i-1][1],dp[i-1][0]))))+a[i];
	}
	ans=dp[n][0];
	for(register int i=1;i<5;i++)ans=min(ans,dp[n][i]);
	printf("%lld\n",ans);
	return 0;
}
```