#include<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define gt getchar()
#define ll long long
#define File(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
inline int in()
{
	int k=0;char ch=gt;
	while(ch<'-')ch=gt;
	while(ch>'-')k=k*10+ch-'0',ch=gt;
	return k;
}
const int N=2e5+5;
const ll inf=1ll<<60;
ll a[N],as[N],x[N],y[N],xs[N],ys[N],L[N],R[N];
inline void cmin(ll &x,ll y){if(x>y)x=y;}
int main()
{
	int n=in();
	for(int i=1;i<=n;++i)a[i]=in(),x[i]=~a[i]&1,y[i]=a[i]<=2?2-a[i]:a[i]&1;
	for(int i=1;i<=n;++i)xs[i]=xs[i-1]+x[i],ys[i]=ys[i-1]+y[i],as[i]=as[i-1]+a[i];
	ll mn=L[0]=R[n]=0;
	for(int i=1;i<=n;++i)cmin(mn,as[i]-ys[i]),L[i]=mn+ys[i];
	mn=ys[n];
	for(int i=n-1;~i;--i)cmin(mn,as[n]-as[i]+ys[i]),R[i]=mn-ys[i];
	ll ans=mn=inf;
	for(int i=0;i<=n;++i)cmin(mn,L[i]-xs[i]),cmin(ans,R[i]+mn+xs[i]);
	printf("%lld\n",ans);
	return 0;
}

### Prompt

Create a solution in Cpp for 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<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define gt getchar()
#define ll long long
#define File(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
inline int in()
{
	int k=0;char ch=gt;
	while(ch<'-')ch=gt;
	while(ch>'-')k=k*10+ch-'0',ch=gt;
	return k;
}
const int N=2e5+5;
const ll inf=1ll<<60;
ll a[N],as[N],x[N],y[N],xs[N],ys[N],L[N],R[N];
inline void cmin(ll &x,ll y){if(x>y)x=y;}
int main()
{
	int n=in();
	for(int i=1;i<=n;++i)a[i]=in(),x[i]=~a[i]&1,y[i]=a[i]<=2?2-a[i]:a[i]&1;
	for(int i=1;i<=n;++i)xs[i]=xs[i-1]+x[i],ys[i]=ys[i-1]+y[i],as[i]=as[i-1]+a[i];
	ll mn=L[0]=R[n]=0;
	for(int i=1;i<=n;++i)cmin(mn,as[i]-ys[i]),L[i]=mn+ys[i];
	mn=ys[n];
	for(int i=n-1;~i;--i)cmin(mn,as[n]-as[i]+ys[i]),R[i]=mn-ys[i];
	ll ans=mn=inf;
	for(int i=0;i<=n;++i)cmin(mn,L[i]-xs[i]),cmin(ans,R[i]+mn+xs[i]);
	printf("%lld\n",ans);
	return 0;
}

```