#include <bits/stdc++.h>
using namespace std;
const int maxn = 234567;
long long f[5][maxn];
long long a[maxn];
int main(){
	int n; cin >> n;
	for(int j = 0; j < 5; j++) f[j][0] = 1ll<<50;
	f[0][0] = 0;
	f[1][0] = 0;
	f[2][0] = 0;
	for(int i = 0; i < n; i++){
		int x; cin >> x;
		f[0][i + 1] = f[0][i] + x;
		f[1][i + 1] = min(f[1][i], f[0][i]) + (x%2) + (x == 0 ? 2 : 0);
		f[2][i + 1] = min(min(f[2][i], f[1][i]), f[0][i]) + 1 - (x%2);
		f[3][i + 1] = min(min(f[1][i], f[0][i]), min(f[2][i], f[3][i])) + (x%2) + (x == 0 ? 2 : 0);
		f[4][i + 1] = min(min(f[4][i], f[3][i]), min(f[2][i], min(f[1][i], f[0][i]))) + x;
	}
	cout << min(f[3][n], min(f[4][n], f[2][n])) << endl;
	return 0;
}

### Prompt

Your challenge is to write a CPP solution 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;
const int maxn = 234567;
long long f[5][maxn];
long long a[maxn];
int main(){
	int n; cin >> n;
	for(int j = 0; j < 5; j++) f[j][0] = 1ll<<50;
	f[0][0] = 0;
	f[1][0] = 0;
	f[2][0] = 0;
	for(int i = 0; i < n; i++){
		int x; cin >> x;
		f[0][i + 1] = f[0][i] + x;
		f[1][i + 1] = min(f[1][i], f[0][i]) + (x%2) + (x == 0 ? 2 : 0);
		f[2][i + 1] = min(min(f[2][i], f[1][i]), f[0][i]) + 1 - (x%2);
		f[3][i + 1] = min(min(f[1][i], f[0][i]), min(f[2][i], f[3][i])) + (x%2) + (x == 0 ? 2 : 0);
		f[4][i + 1] = min(min(f[4][i], f[3][i]), min(f[2][i], min(f[1][i], f[0][i]))) + x;
	}
	cout << min(f[3][n], min(f[4][n], f[2][n])) << endl;
	return 0;
}

```