#include <bits/stdc++.h>
using namespace std;
const long long MAXn = 2e5 + 10, INF = 1e18;

long long dp[MAXn][6], ar[MAXn], n;

int main() {
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> ar[i];
	for (int i = 0; i < n; i++) {
		if (i) {
			for (int j = 0; j < 5; j++) {
				dp[i][j] = INF;
				for (int x = 0; x <= j; x++)
					dp[i][j] = min(dp[i-1][x], dp[i][j]);
			}
		}
		dp[i][0] += (ar[i]);
		if (ar[i] == 0) {
			dp[i][3] += 2;
			dp[i][1] += 2;
		}
		else {
			dp[i][1] += (ar[i] % 2 == 1);
			dp[i][3] += (ar[i] % 2 == 1);		
		}
		dp[i][2] += (ar[i] % 2 == 0);
		dp[i][4] += (ar[i]);
	}
	long long ans = MAXn;
	for (int i = 0; i < 5; i++)
		ans = min(ans, dp[n-1][i]);
	cout << ans;
}

### Prompt

In Cpp, your task is to solve 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 long long MAXn = 2e5 + 10, INF = 1e18;

long long dp[MAXn][6], ar[MAXn], n;

int main() {
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> ar[i];
	for (int i = 0; i < n; i++) {
		if (i) {
			for (int j = 0; j < 5; j++) {
				dp[i][j] = INF;
				for (int x = 0; x <= j; x++)
					dp[i][j] = min(dp[i-1][x], dp[i][j]);
			}
		}
		dp[i][0] += (ar[i]);
		if (ar[i] == 0) {
			dp[i][3] += 2;
			dp[i][1] += 2;
		}
		else {
			dp[i][1] += (ar[i] % 2 == 1);
			dp[i][3] += (ar[i] % 2 == 1);		
		}
		dp[i][2] += (ar[i] % 2 == 0);
		dp[i][4] += (ar[i]);
	}
	long long ans = MAXn;
	for (int i = 0; i < 5; i++)
		ans = min(ans, dp[n-1][i]);
	cout << ans;
}

```