/*


*/
#include <cstdio>
#include <cctype>
#include <algorithm>
//#define gc() getchar()
#define MAXIN 500000
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
typedef long long LL;
const int N=2e5+5;

char IN[MAXIN],*SS=IN,*TT=IN;

inline int read()
{
	int now=0;register char c=gc();
	for(;!isdigit(c);c=gc());
	for(;isdigit(c);now=now*10+c-48,c=gc());
	return now;
}

int main()
{
	int n=read(); LL f[5]={0};
	for(int i=1; i<=n; ++i)
	{
		int ai=read();
		LL mn=f[0]; f[0]=f[0]+ai;
		mn=std::min(mn,f[1]), f[1]=mn+(ai?ai&1:2);
		mn=std::min(mn,f[2]), f[2]=mn+(ai?ai+1&1:1);
		mn=std::min(mn,f[3]), f[3]=mn+(ai?ai&1:2);
		mn=std::min(mn,f[4]), f[4]=mn+ai;
	}
	printf("%lld\n",std::min(f[2],std::min(f[3],f[4])));

	return 0;
}
### Prompt

Your task is to create 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 <cstdio>
#include <cctype>
#include <algorithm>
//#define gc() getchar()
#define MAXIN 500000
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
typedef long long LL;
const int N=2e5+5;

char IN[MAXIN],*SS=IN,*TT=IN;

inline int read()
{
	int now=0;register char c=gc();
	for(;!isdigit(c);c=gc());
	for(;isdigit(c);now=now*10+c-48,c=gc());
	return now;
}

int main()
{
	int n=read(); LL f[5]={0};
	for(int i=1; i<=n; ++i)
	{
		int ai=read();
		LL mn=f[0]; f[0]=f[0]+ai;
		mn=std::min(mn,f[1]), f[1]=mn+(ai?ai&1:2);
		mn=std::min(mn,f[2]), f[2]=mn+(ai?ai+1&1:1);
		mn=std::min(mn,f[3]), f[3]=mn+(ai?ai&1:2);
		mn=std::min(mn,f[4]), f[4]=mn+ai;
	}
	printf("%lld\n",std::min(f[2],std::min(f[3],f[4])));

	return 0;
}
```