#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;

const long long INF = 1LL<<60;

int score(int x, int z){
	if(z == 0 || z == 4){
		return x;
	}else if(z == 1 || z == 3){
		if(x > 0){
			return x % 2;
		}else{
			return 2;
		}
	}else{
		return (x + 1) % 2;
	}
}

int main(){
	int n;
	cin >> n;
	vector<int> a(n);
	for(int i = 0; i < n; i++){
		cin >> a[i];
	}
	vector<vector<long long>> dp(n + 1, vector<long long>(5, INF));
	dp[0][0] = 0;
	for(int i = 0; i < n; i++){
		for(int j = 0; j < 5; j++){
			for(int k = 0; k <= j; k++){
				dp[i + 1][j] = min(dp[i + 1][j], dp[i][k] + score(a[i], j));
			}
		}
	}
	long long ans = INF;
	for(int i = 0; i < 5; i++){
		ans = min(ans, dp[n][i]);
	}
	cout << ans << endl;
	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<iostream>
#include<vector>
#include<algorithm>

using namespace std;

const long long INF = 1LL<<60;

int score(int x, int z){
	if(z == 0 || z == 4){
		return x;
	}else if(z == 1 || z == 3){
		if(x > 0){
			return x % 2;
		}else{
			return 2;
		}
	}else{
		return (x + 1) % 2;
	}
}

int main(){
	int n;
	cin >> n;
	vector<int> a(n);
	for(int i = 0; i < n; i++){
		cin >> a[i];
	}
	vector<vector<long long>> dp(n + 1, vector<long long>(5, INF));
	dp[0][0] = 0;
	for(int i = 0; i < n; i++){
		for(int j = 0; j < 5; j++){
			for(int k = 0; k <= j; k++){
				dp[i + 1][j] = min(dp[i + 1][j], dp[i][k] + score(a[i], j));
			}
		}
	}
	long long ans = INF;
	for(int i = 0; i < 5; i++){
		ans = min(ans, dp[n][i]);
	}
	cout << ans << endl;
	return 0;
}

```