/* به نام یزدان */
#include <bits/stdc++.h>
using namespace std;

const int MAX_N = 200 * 1000 + 5;
long long n, a[MAX_N], dp[MAX_N][5];

void read_input() {
	cin >> n;
	for (int i = 1; i <= n; i++)
		cin >> a[i];
}

void solve() {
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= 3; j++) {
			int x = a[i] - 1 - j % 2;
			if (x < 0)
				x += a[i];
			else
				x = a[i] - x % 2;
			dp[i][j] = max(dp[i][j - 1], dp[i - 1][j] + x);	
		}
}

void print_output() {
	long long ans = 0;
	for (int i = 1; i <= n; i++)
		ans = min(ans, -dp[i][3]);
	for (int i = 1; i <= n; i++)
		ans += a[i];
	cout << ans;
}

int main() {
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	read_input();
	solve();
	print_output();
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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
/* به نام یزدان */
#include <bits/stdc++.h>
using namespace std;

const int MAX_N = 200 * 1000 + 5;
long long n, a[MAX_N], dp[MAX_N][5];

void read_input() {
	cin >> n;
	for (int i = 1; i <= n; i++)
		cin >> a[i];
}

void solve() {
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= 3; j++) {
			int x = a[i] - 1 - j % 2;
			if (x < 0)
				x += a[i];
			else
				x = a[i] - x % 2;
			dp[i][j] = max(dp[i][j - 1], dp[i - 1][j] + x);	
		}
}

void print_output() {
	long long ans = 0;
	for (int i = 1; i <= n; i++)
		ans = min(ans, -dp[i][3]);
	for (int i = 1; i <= n; i++)
		ans += a[i];
	cout << ans;
}

int main() {
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	read_input();
	solve();
	print_output();
}

```