#include <vector>
#include<iostream>
#include <cmath>
using namespace std;

int main(void){
	int n;
	long a[200000];
	cin >> n;
	for(int i=0;i<n;i++) cin >> a[i];
	long **dp;
	dp = (long**)malloc(sizeof(long*)*(n+1));
	for(int i=0;i<=n;i++) {
		dp[i] = (long*)malloc(sizeof(long)*5);
		for(int j=0;j<5;j++)dp[i][j] = 1000000000;
	}
for(int i=0;i<=5;i++)dp[0][i] = 0;
	for(int i=1;i<=n;i++){
		dp[i][0] = dp[i-1][0] + a[i-1];
		for(int j=1;j<5;j++){
			for(int k=0;k<=j;k++){
				dp[i][j] = min(dp[i][j], dp[i-1][k]);
			}
		}
		dp[i][1] += (a[i-1] == 0 ? 2 : (a[i-1] & 1));
		dp[i][2] += (a[i-1] % 2 == 0);
		dp[i][3] += (a[i-1] == 0 ? 2 : (a[i-1] & 1));
		dp[i][4] += a[i-1];
	}
	long ans = 1000000000;
	for(int i=0;i<5;i++) ans = min(ans, dp[n][i]);
	cout << ans << endl;
	return 0;
}
### Prompt

Your task is to create 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 <vector>
#include<iostream>
#include <cmath>
using namespace std;

int main(void){
	int n;
	long a[200000];
	cin >> n;
	for(int i=0;i<n;i++) cin >> a[i];
	long **dp;
	dp = (long**)malloc(sizeof(long*)*(n+1));
	for(int i=0;i<=n;i++) {
		dp[i] = (long*)malloc(sizeof(long)*5);
		for(int j=0;j<5;j++)dp[i][j] = 1000000000;
	}
for(int i=0;i<=5;i++)dp[0][i] = 0;
	for(int i=1;i<=n;i++){
		dp[i][0] = dp[i-1][0] + a[i-1];
		for(int j=1;j<5;j++){
			for(int k=0;k<=j;k++){
				dp[i][j] = min(dp[i][j], dp[i-1][k]);
			}
		}
		dp[i][1] += (a[i-1] == 0 ? 2 : (a[i-1] & 1));
		dp[i][2] += (a[i-1] % 2 == 0);
		dp[i][3] += (a[i-1] == 0 ? 2 : (a[i-1] & 1));
		dp[i][4] += a[i-1];
	}
	long ans = 1000000000;
	for(int i=0;i<5;i++) ans = min(ans, dp[n][i]);
	cout << ans << endl;
	return 0;
}
```