#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

ll a[200009], p[200009], l[200009], lm[200009], r[200009];

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);	
	int n; cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		if (a[i] == 0) p[i] = 2;
		else p[i] = a[i] % 2;
	}
	ll s = 0;
	for (int i = 1; i <= n; i++) {
		s += a[i];
		l[i] = min(l[i - 1] + p[i], s);
	}
	s = 0;
	for (int i = n; i >= 1; i--) {
		s += a[i];
		r[i] = min(r[i + 1] + p[i], s);
	}
	s = 0;
	for (int i = 0; i <= n + 1; i++) {
		if (1 <= i && i <= n && p[i] != 1) s++;
		l[i] -= s; r[i + 1] += s;
	}
	lm[0] = l[0];
	for (int i = 1; i <= n; i++)
		lm[i] = min(lm[i - 1], l[i]);
	ll ans = lm[0] + r[1];
	for (int i = 1; i <= n + 1; i++)
		ans = min(ans, lm[i - 1] + r[i]);
	cout << ans << '\n';
	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 <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

ll a[200009], p[200009], l[200009], lm[200009], r[200009];

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);	
	int n; cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		if (a[i] == 0) p[i] = 2;
		else p[i] = a[i] % 2;
	}
	ll s = 0;
	for (int i = 1; i <= n; i++) {
		s += a[i];
		l[i] = min(l[i - 1] + p[i], s);
	}
	s = 0;
	for (int i = n; i >= 1; i--) {
		s += a[i];
		r[i] = min(r[i + 1] + p[i], s);
	}
	s = 0;
	for (int i = 0; i <= n + 1; i++) {
		if (1 <= i && i <= n && p[i] != 1) s++;
		l[i] -= s; r[i + 1] += s;
	}
	lm[0] = l[0];
	for (int i = 1; i <= n; i++)
		lm[i] = min(lm[i - 1], l[i]);
	ll ans = lm[0] + r[1];
	for (int i = 1; i <= n + 1; i++)
		ans = min(ans, lm[i - 1] + r[i]);
	cout << ans << '\n';
	return 0;
}
```