#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
#define maxn 200020
using namespace std;
inline int getint(){
    char c=getchar();int x=0;bool p=0;
    while((c>'9'||c<'0')&&c!='-')c=getchar();
    if(c=='-')p=1,c=getchar();
    while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();
    if(p)x=-x;return x;
}
int w[maxn];
ll dp[maxn][5],s[maxn],rs[maxn];
int main(){
	int n=getint();s[0]=0;rs[n+1]=0;
	for(int i=1;i<=n;++i)w[i]=s[i]=rs[i]=getint();
	for(int i=2;i<=n;++i)s[i]+=s[i-1];
	for(int i=n-1;i>=1;--i)rs[i]+=rs[i+1];
	memset(dp,0,sizeof(dp));
	ll ans=rs[1]; 
	for(int i=1;i<=n;++i){
		dp[i][1]=min(dp[i-1][1],s[i-1])+(w[i]&1)+((w[i]==0)*2);
		dp[i][2]=min(s[i-1],min(dp[i-1][1],dp[i-1][2]))+((w[i]&1)^1);
		dp[i][3]=min(dp[i-1][2],dp[i-1][3])+(w[i]&1)+((w[i]==0)*2);
		for(int j=1;j<=3;++j)ans=min(ans,dp[i][j]+rs[i+1]);
	}
	cout<<ans<<endl;
	return 0;
}
### Prompt

Please formulate 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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
#define maxn 200020
using namespace std;
inline int getint(){
    char c=getchar();int x=0;bool p=0;
    while((c>'9'||c<'0')&&c!='-')c=getchar();
    if(c=='-')p=1,c=getchar();
    while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();
    if(p)x=-x;return x;
}
int w[maxn];
ll dp[maxn][5],s[maxn],rs[maxn];
int main(){
	int n=getint();s[0]=0;rs[n+1]=0;
	for(int i=1;i<=n;++i)w[i]=s[i]=rs[i]=getint();
	for(int i=2;i<=n;++i)s[i]+=s[i-1];
	for(int i=n-1;i>=1;--i)rs[i]+=rs[i+1];
	memset(dp,0,sizeof(dp));
	ll ans=rs[1]; 
	for(int i=1;i<=n;++i){
		dp[i][1]=min(dp[i-1][1],s[i-1])+(w[i]&1)+((w[i]==0)*2);
		dp[i][2]=min(s[i-1],min(dp[i-1][1],dp[i-1][2]))+((w[i]&1)^1);
		dp[i][3]=min(dp[i-1][2],dp[i-1][3])+(w[i]&1)+((w[i]==0)*2);
		for(int j=1;j<=3;++j)ans=min(ans,dp[i][j]+rs[i+1]);
	}
	cout<<ans<<endl;
	return 0;
}
```