#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

#define Maxn 200005

long long n, a[Maxn], dp[Maxn][3], sum, ans;

int main() {
	register int i;
	scanf("%lld", &n);
	memset(dp, 0x3f, sizeof(dp));
	for (dp[0][0] = 0, i = 1; i <= n; i ++) {
		scanf("%lld", a + i);
		dp[i][0] = min(dp[i - 1][0], sum) + (a[i] & 1 ? 1 : (a[i] ? 0 : 2));
		dp[i][1] = min(dp[i - 1][1], dp[i - 1][2]) + (a[i] & 1 ? 1 : (a[i] ? 0 : 2));
		dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][2], sum)) + (a[i] & 1 ? 0 : 1);
		sum += a[i];
	}
	for (sum = 0, ans = 1e18, i = n; i >= 0; i --)
		ans = min(ans, min({dp[i][0], dp[i][1], dp[i][2]}) + (sum += a[i + 1]));
	printf("%lld\n",ans);
	return 0;
}
### 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 <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

#define Maxn 200005

long long n, a[Maxn], dp[Maxn][3], sum, ans;

int main() {
	register int i;
	scanf("%lld", &n);
	memset(dp, 0x3f, sizeof(dp));
	for (dp[0][0] = 0, i = 1; i <= n; i ++) {
		scanf("%lld", a + i);
		dp[i][0] = min(dp[i - 1][0], sum) + (a[i] & 1 ? 1 : (a[i] ? 0 : 2));
		dp[i][1] = min(dp[i - 1][1], dp[i - 1][2]) + (a[i] & 1 ? 1 : (a[i] ? 0 : 2));
		dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][2], sum)) + (a[i] & 1 ? 0 : 1);
		sum += a[i];
	}
	for (sum = 0, ans = 1e18, i = n; i >= 0; i --)
		ans = min(ans, min({dp[i][0], dp[i][1], dp[i][2]}) + (sum += a[i + 1]));
	printf("%lld\n",ans);
	return 0;
}
```