#include<bits/stdc++.h>
#define int long long
#define N 2000005
using namespace std;
int n,a[N],dp[N][6];
signed main(){
	scanf("%lld",&n);
	for (int i=1;i<=n;i++) scanf("%lld",&a[i]);
	for (int i=1;i<=n;i++){
		dp[i][1]=dp[i-1][1]+a[i];
		if (a[i]%2){
			dp[i][2]=min(dp[i][1],dp[i-1][2]+1);
			dp[i][3]=min(dp[i][2],dp[i-1][3]);
			dp[i][4]=min(dp[i][3],dp[i-1][4]+1);
		}
		else {
			if (!a[i]){
				dp[i][2]=min(dp[i][1],dp[i-1][2]+2);
				dp[i][3]=min(dp[i][2],dp[i-1][3]+1);
				dp[i][4]=min(dp[i][3],dp[i-1][4]+2);
			}
			else {
				dp[i][2]=min(dp[i][1],dp[i-1][2]);
				dp[i][3]=min(dp[i][2],dp[i-1][3]+1);
				dp[i][4]=min(dp[i][3],dp[i-1][4]);
			}
		} 
		dp[i][5]=min(dp[i][4],dp[i-1][5]+a[i]);
	}
	printf("%lld\n",dp[n][5]);
	return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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 int long long
#define N 2000005
using namespace std;
int n,a[N],dp[N][6];
signed main(){
	scanf("%lld",&n);
	for (int i=1;i<=n;i++) scanf("%lld",&a[i]);
	for (int i=1;i<=n;i++){
		dp[i][1]=dp[i-1][1]+a[i];
		if (a[i]%2){
			dp[i][2]=min(dp[i][1],dp[i-1][2]+1);
			dp[i][3]=min(dp[i][2],dp[i-1][3]);
			dp[i][4]=min(dp[i][3],dp[i-1][4]+1);
		}
		else {
			if (!a[i]){
				dp[i][2]=min(dp[i][1],dp[i-1][2]+2);
				dp[i][3]=min(dp[i][2],dp[i-1][3]+1);
				dp[i][4]=min(dp[i][3],dp[i-1][4]+2);
			}
			else {
				dp[i][2]=min(dp[i][1],dp[i-1][2]);
				dp[i][3]=min(dp[i][2],dp[i-1][3]+1);
				dp[i][4]=min(dp[i][3],dp[i-1][4]);
			}
		} 
		dp[i][5]=min(dp[i][4],dp[i-1][5]+a[i]);
	}
	printf("%lld\n",dp[n][5]);
	return 0;
}
```