#include <bits/stdc++.h>
#define mod 1000000007
#define sp ' '
#define intmax 2147483647
#define llmax 9223372036854775807
#define mkp make_pair
typedef long long ll;
using namespace std;

ll N, A[200000], Lev[200001], Lod[200001], Rev[200001], S, MIN;

int main() {
	cin >> N;
	for (int i = 0; i < N; ++i) {
		cin >> A[i];
	}
	Lev[0] = Lod[0] = 0;
	for (int i = 0; i < N; ++i) {
		S += A[i];
		if (A[i]) {
			Lev[i + 1] = min(S, Lev[i] + A[i] % 2);
			Lod[i + 1] = min(Lev[i + 1], Lod[i] + (A[i] + 1) % 2);
		}
		else {
			Lev[i + 1] = min(S, Lev[i] + 2);
			Lod[i + 1] = min(Lev[i + 1], Lod[i] + (A[i] + 1) % 2);
		}
	}
	S = 0;
	for (int i = N - 1; i >= 0; --i) {
		S += A[i];
		if (A[i]) {
			Rev[i] = min(S, Rev[i + 1] + A[i] % 2);
		}
		else {
			Rev[i] = min(S, Rev[i + 1] + 2);
		}
	}
	MIN = llmax;
	for (int i = 0; i <= N; ++i) {
		MIN = min(MIN, Lod[i] + Rev[i]);
	}
	cout << MIN << endl;
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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 mod 1000000007
#define sp ' '
#define intmax 2147483647
#define llmax 9223372036854775807
#define mkp make_pair
typedef long long ll;
using namespace std;

ll N, A[200000], Lev[200001], Lod[200001], Rev[200001], S, MIN;

int main() {
	cin >> N;
	for (int i = 0; i < N; ++i) {
		cin >> A[i];
	}
	Lev[0] = Lod[0] = 0;
	for (int i = 0; i < N; ++i) {
		S += A[i];
		if (A[i]) {
			Lev[i + 1] = min(S, Lev[i] + A[i] % 2);
			Lod[i + 1] = min(Lev[i + 1], Lod[i] + (A[i] + 1) % 2);
		}
		else {
			Lev[i + 1] = min(S, Lev[i] + 2);
			Lod[i + 1] = min(Lev[i + 1], Lod[i] + (A[i] + 1) % 2);
		}
	}
	S = 0;
	for (int i = N - 1; i >= 0; --i) {
		S += A[i];
		if (A[i]) {
			Rev[i] = min(S, Rev[i + 1] + A[i] % 2);
		}
		else {
			Rev[i] = min(S, Rev[i + 1] + 2);
		}
	}
	MIN = llmax;
	for (int i = 0; i <= N; ++i) {
		MIN = min(MIN, Lod[i] + Rev[i]);
	}
	cout << MIN << endl;
	return 0;
}
```