#include <bits/stdc++.h>
#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
//#define int long long
typedef long long ll;
const int MOD = 1000000007;
const int INF = 1010000000;
const double EPS = 1e-10;
using namespace std;
const pair<int,int> fd[] = {make_pair(1,0),make_pair(-1,0),make_pair(0,1),make_pair(0,-1)}; 

signed main() {
  ll l;cin>>l;
  ll dp[200001][5];rep(i,5)dp[0][i] = 0;
  repd(i,1,l+1){
    ll a;cin>>a;
    dp[i][0] = dp[i-1][0]+a;
    dp[i][1] = min(dp[i-1][1]+(a==0 ? 2 : a % 2), dp[i][0]);
    dp[i][2] = min(dp[i-1][2]+((a+1) % 2), dp[i][1]);
    dp[i][3] = min(dp[i-1][3]+(a==0 ? 2 : a % 2), dp[i][2]);
    dp[i][4] = min(dp[i-1][4]+a, dp[i][3]);
  }
  cout << dp[l][4] << 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>
#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
//#define int long long
typedef long long ll;
const int MOD = 1000000007;
const int INF = 1010000000;
const double EPS = 1e-10;
using namespace std;
const pair<int,int> fd[] = {make_pair(1,0),make_pair(-1,0),make_pair(0,1),make_pair(0,-1)}; 

signed main() {
  ll l;cin>>l;
  ll dp[200001][5];rep(i,5)dp[0][i] = 0;
  repd(i,1,l+1){
    ll a;cin>>a;
    dp[i][0] = dp[i-1][0]+a;
    dp[i][1] = min(dp[i-1][1]+(a==0 ? 2 : a % 2), dp[i][0]);
    dp[i][2] = min(dp[i-1][2]+((a+1) % 2), dp[i][1]);
    dp[i][3] = min(dp[i-1][3]+(a==0 ? 2 : a % 2), dp[i][2]);
    dp[i][4] = min(dp[i-1][4]+a, dp[i][3]);
  }
  cout << dp[l][4] << endl;
}

```