#include <iostream>
using namespace std;

#define INF ((unsigned long long)200000*200000)
unsigned long long A[200000] = {0};
unsigned long long dp[200001][5];


unsigned long long cost(int i, int k) {
	if (k==0 || k==4) return A[i];
	if (k==1 || k==3) {
		if (A[i]==0) return 2;
		if ((A[i]&0x1)==0) return 0;
		return 1;
	}
	if ((A[i]&0x1)==1) return 0;
	return 1;
}

int main(void) {
	int L;
	cin >> L;
	for (int i = 0; i < L; i++) cin >> A[i];

	for (int i = 0; i <= L; i++) {
		for (int j = 0; j < 5; j++) {
			dp[i][j] = INF;
		}
	}

	dp[0][0] = 0;
	for (int i = 0; i < L; i++) {
		for (int j = 0; j < 5; j++) {
			for (int k = j; k < 5; k++) {
				dp[i+1][k] = min(dp[i+1][k], dp[i][j] + cost(i, k));
			}
		}
	}

	unsigned long long ans = INF;
	for (int i = 0; i < 5; i++) {
		ans = min(ans, dp[L][i]);
	}
	cout << ans << endl;

	return 0;
}

### Prompt

Your challenge is to write 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 <iostream>
using namespace std;

#define INF ((unsigned long long)200000*200000)
unsigned long long A[200000] = {0};
unsigned long long dp[200001][5];


unsigned long long cost(int i, int k) {
	if (k==0 || k==4) return A[i];
	if (k==1 || k==3) {
		if (A[i]==0) return 2;
		if ((A[i]&0x1)==0) return 0;
		return 1;
	}
	if ((A[i]&0x1)==1) return 0;
	return 1;
}

int main(void) {
	int L;
	cin >> L;
	for (int i = 0; i < L; i++) cin >> A[i];

	for (int i = 0; i <= L; i++) {
		for (int j = 0; j < 5; j++) {
			dp[i][j] = INF;
		}
	}

	dp[0][0] = 0;
	for (int i = 0; i < L; i++) {
		for (int j = 0; j < 5; j++) {
			for (int k = j; k < 5; k++) {
				dp[i+1][k] = min(dp[i+1][k], dp[i][j] + cost(i, k));
			}
		}
	}

	unsigned long long ans = INF;
	for (int i = 0; i < 5; i++) {
		ans = min(ans, dp[L][i]);
	}
	cout << ans << endl;

	return 0;
}

```