#include <bits/stdc++.h>

using namespace std;
using ll = long long;

int main() {
	const ll INF = 1e18;
	ll L;
	cin >> L;
	vector<ll> A(L + 1);
	for (int i = 1; i <= L; ++i) { cin >> A[i]; }

	vector<vector<ll>> dp(L + 1, vector<ll>(5, INF));
	dp[1][0] = A[1];
	dp[1][1] = A[1] % 2;
	if (A[1] == 0) { dp[1][1] = 2; }
	dp[1][2] = 1 - (A[1] % 2);
	for (int i = 2; i <= L; ++i) {
		for (int j = 0; j < 5; ++j) {
			ll tmp = INF;
			for (int k = 0; k <= j; ++k) { tmp = min(tmp, dp[i - 1][k]); }

			dp[i][j] = tmp;
			if ((j == 0) || (j == 4)) { dp[i][j] += A[i]; }
			if ((j == 1) || (j == 3)) { 
				if (A[i] == 0) { dp[i][j] += 2; }
				else { dp[i][j] += (A[i] % 2); }
			}
			if (j == 2) {
				dp[i][j] += (1 - (A[i] % 2));
			}
		}
	}

	ll res = INF;
	for (int i = 0; i < 5; ++i) { res = min(res, dp[L][i]); }

	cout << res << endl;

	return 0;
}

### 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
#include <bits/stdc++.h>

using namespace std;
using ll = long long;

int main() {
	const ll INF = 1e18;
	ll L;
	cin >> L;
	vector<ll> A(L + 1);
	for (int i = 1; i <= L; ++i) { cin >> A[i]; }

	vector<vector<ll>> dp(L + 1, vector<ll>(5, INF));
	dp[1][0] = A[1];
	dp[1][1] = A[1] % 2;
	if (A[1] == 0) { dp[1][1] = 2; }
	dp[1][2] = 1 - (A[1] % 2);
	for (int i = 2; i <= L; ++i) {
		for (int j = 0; j < 5; ++j) {
			ll tmp = INF;
			for (int k = 0; k <= j; ++k) { tmp = min(tmp, dp[i - 1][k]); }

			dp[i][j] = tmp;
			if ((j == 0) || (j == 4)) { dp[i][j] += A[i]; }
			if ((j == 1) || (j == 3)) { 
				if (A[i] == 0) { dp[i][j] += 2; }
				else { dp[i][j] += (A[i] % 2); }
			}
			if (j == 2) {
				dp[i][j] += (1 - (A[i] % 2));
			}
		}
	}

	ll res = INF;
	for (int i = 0; i < 5; ++i) { res = min(res, dp[L][i]); }

	cout << res << endl;

	return 0;
}

```