#include <bits/stdc++.h>
using namespace std;

#define INF (INT64_MAX)
#define MOD (1000000000+7)
#define MAX 200000

int L;
long long A[MAX];

long long dp[MAX + 1][5];

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

	for( int i = 0; i < L; i++ ) {
		int zero_c = 0;
		if( A[i] == 0 ) {
			zero_c = 2;
		}
		dp[i + 1][0] = dp[i][0] + A[i];
		dp[i + 1][1] = min( dp[i][0], dp[i][1] ) + A[i] % 2 + zero_c;
		dp[i + 1][2] = min( dp[i][2], min( dp[i][0], dp[i][1] ) ) + (A[i] + 1) % 2;
		dp[i + 1][3] = min( dp[i][3], min( dp[i][2], min( dp[i][0], dp[i][1] ) ) ) + A[i] % 2 + zero_c;
		dp[i + 1][4] = min( dp[i][4], min( dp[i][3], min( dp[i][2], min( dp[i][0], dp[i][1] ) ) ) ) + A[i];
	}
	long long ans = INF;
	for( int i = 0; i < 5; i++ ) {
		ans = min( ans, dp[L][i] );
	}

	cout << ans << endl;

	return 0;
}

### Prompt

Please formulate 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 namespace std;

#define INF (INT64_MAX)
#define MOD (1000000000+7)
#define MAX 200000

int L;
long long A[MAX];

long long dp[MAX + 1][5];

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

	for( int i = 0; i < L; i++ ) {
		int zero_c = 0;
		if( A[i] == 0 ) {
			zero_c = 2;
		}
		dp[i + 1][0] = dp[i][0] + A[i];
		dp[i + 1][1] = min( dp[i][0], dp[i][1] ) + A[i] % 2 + zero_c;
		dp[i + 1][2] = min( dp[i][2], min( dp[i][0], dp[i][1] ) ) + (A[i] + 1) % 2;
		dp[i + 1][3] = min( dp[i][3], min( dp[i][2], min( dp[i][0], dp[i][1] ) ) ) + A[i] % 2 + zero_c;
		dp[i + 1][4] = min( dp[i][4], min( dp[i][3], min( dp[i][2], min( dp[i][0], dp[i][1] ) ) ) ) + A[i];
	}
	long long ans = INF;
	for( int i = 0; i < 5; i++ ) {
		ans = min( ans, dp[L][i] );
	}

	cout << ans << endl;

	return 0;
}

```