#include <bits/stdc++.h>
using i64 = long long;
using std::cout;
using std::endl;
using std::cin;

int main() {
	int n; scanf("%d", &n); std::vector<i64> a(n), b(n);
	for(int i = 0; i < n; i++) {
		scanf("%lld", &a[i]);
		
		if(a[i] == 0) continue;
		if(a[i] % 2) b[i] = 1;
		else b[i] = 2;
	}
	
	std::vector<std::vector<i64>> dp(n + 1, std::vector<i64>(5, 1LL << 60));
	for(int i = 0; i < 5; i++) dp[0][i] = 0;
	for(int i = 0; i < n; i++) {
		dp[i + 1][0] = dp[i][0] + a[i];
		dp[i + 1][1] = std::min(dp[i][1], dp[i][0]) + std::abs(b[i] - 2);
		dp[i + 1][2] = std::min({dp[i][2], dp[i][1], dp[i][0]}) + std::abs(b[i] - 1);
		dp[i + 1][3] = std::min({dp[i][3], dp[i][2], dp[i][1], dp[i][0]}) + std::abs(b[i] - 2);
		dp[i + 1][4] = std::min({dp[i][4], dp[i][3], dp[i][2], dp[i][1], dp[i][0]}) + a[i];
	}
	printf("%lld\n", std::min({dp[n][0], dp[n][1], dp[n][2], dp[n][3], dp[n][4]}));
	return 0;
}

### Prompt

Generate 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 i64 = long long;
using std::cout;
using std::endl;
using std::cin;

int main() {
	int n; scanf("%d", &n); std::vector<i64> a(n), b(n);
	for(int i = 0; i < n; i++) {
		scanf("%lld", &a[i]);
		
		if(a[i] == 0) continue;
		if(a[i] % 2) b[i] = 1;
		else b[i] = 2;
	}
	
	std::vector<std::vector<i64>> dp(n + 1, std::vector<i64>(5, 1LL << 60));
	for(int i = 0; i < 5; i++) dp[0][i] = 0;
	for(int i = 0; i < n; i++) {
		dp[i + 1][0] = dp[i][0] + a[i];
		dp[i + 1][1] = std::min(dp[i][1], dp[i][0]) + std::abs(b[i] - 2);
		dp[i + 1][2] = std::min({dp[i][2], dp[i][1], dp[i][0]}) + std::abs(b[i] - 1);
		dp[i + 1][3] = std::min({dp[i][3], dp[i][2], dp[i][1], dp[i][0]}) + std::abs(b[i] - 2);
		dp[i + 1][4] = std::min({dp[i][4], dp[i][3], dp[i][2], dp[i][1], dp[i][0]}) + a[i];
	}
	printf("%lld\n", std::min({dp[n][0], dp[n][1], dp[n][2], dp[n][3], dp[n][4]}));
	return 0;
}

```