#include <bits/stdc++.h>

#ifdef NON_SUBMIT
#define TEST(n) (n)
#define tout cerr
#else
#define TEST(n) ((void)0)
#define tout cin
#endif

using namespace std;

long long D[5];

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);
	TEST(freopen("input.txt", "r", stdin));
	TEST(freopen("output.txt", "w", stdout));
	TEST(freopen("debug.txt", "w", stderr));
	int N, A;
	long long ans;
	D[1]=D[2]=D[3]=D[4]=0x7fffffff;
	for(cin>>N;N;N--) {
		cin>>A;
		D[4]=min(D[4],min(D[3],min(D[2],min(D[1],D[0]))))+A;
		D[3]=min(D[3],min(D[2],min(D[1],D[0])))+(A ? (A&1):2);
		D[2]=min(D[2],min(D[1],D[0]))+!(A&1);
		D[1]=min(D[1],D[0])+(A ? (A&1):2);
		D[0]+=A;
	}
	ans=D[0];
	for(int i=1;i<5;i++) ans=min(ans,D[i]);
	cout<<ans<<'\n';
	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>

#ifdef NON_SUBMIT
#define TEST(n) (n)
#define tout cerr
#else
#define TEST(n) ((void)0)
#define tout cin
#endif

using namespace std;

long long D[5];

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);
	TEST(freopen("input.txt", "r", stdin));
	TEST(freopen("output.txt", "w", stdout));
	TEST(freopen("debug.txt", "w", stderr));
	int N, A;
	long long ans;
	D[1]=D[2]=D[3]=D[4]=0x7fffffff;
	for(cin>>N;N;N--) {
		cin>>A;
		D[4]=min(D[4],min(D[3],min(D[2],min(D[1],D[0]))))+A;
		D[3]=min(D[3],min(D[2],min(D[1],D[0])))+(A ? (A&1):2);
		D[2]=min(D[2],min(D[1],D[0]))+!(A&1);
		D[1]=min(D[1],D[0])+(A ? (A&1):2);
		D[0]+=A;
	}
	ans=D[0];
	for(int i=1;i<5;i++) ans=min(ans,D[i]);
	cout<<ans<<'\n';
	return 0;
}
```