#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=1LL<<62;

int main() {
  ll l;
  cin >> l;
  vec a(l);
  for(ll i=0;i<l;i++) {
    cin >> a[i];
  }
  ll sum=0;
  for(ll i=0;i<l;i++) {
    sum+=a[i];
  }
  ll ans=sum;
  vec dp(4);
  for(ll i=0;i<l;i++) {
    dp[3]=min({dp[0],dp[1],dp[2],dp[3]})+(a[i]==0?2:a[i]%2);
    dp[2]=min({dp[0],dp[1],dp[2]})+(a[i]+1)%2;
    dp[1]=min(dp[0],dp[1])+(a[i]==0?2:a[i]%2);
    dp[0]+=a[i];
    ans=min(ans,min({dp[0],dp[1],dp[2],dp[3]})+sum-dp[0]);
  }
  cout << ans << endl;
}
### Prompt

Please create a solution in Cpp 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<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=1LL<<62;

int main() {
  ll l;
  cin >> l;
  vec a(l);
  for(ll i=0;i<l;i++) {
    cin >> a[i];
  }
  ll sum=0;
  for(ll i=0;i<l;i++) {
    sum+=a[i];
  }
  ll ans=sum;
  vec dp(4);
  for(ll i=0;i<l;i++) {
    dp[3]=min({dp[0],dp[1],dp[2],dp[3]})+(a[i]==0?2:a[i]%2);
    dp[2]=min({dp[0],dp[1],dp[2]})+(a[i]+1)%2;
    dp[1]=min(dp[0],dp[1])+(a[i]==0?2:a[i]%2);
    dp[0]+=a[i];
    ans=min(ans,min({dp[0],dp[1],dp[2],dp[3]})+sum-dp[0]);
  }
  cout << ans << endl;
}
```