#include<bits/stdc++.h>
typedef long long LL;
using namespace std;
auto no = [](){cout << "NO"; exit(0);};
auto read = [](){int x; cin >> x; return x;};
#define maxn 240000
LL A[maxn];
LL f[5][maxn];
int main(){
	ios::sync_with_stdio(false);
	int N;
	cin >> N;
	for(int i = 1; i <= N; i += 1) cin >> A[i];
	for(int i = 1; i <= N; i += 1){
		LL m = 1E18;
		for(int j = 0; j < 5; j += 1){
			m = min(f[j][i - 1], m);
			f[j][i] = m;
			if(j == 0) f[j][i] += A[i];
			if(j == 1) f[j][i] += A[i] ? A[i] % 2 : 2;
			if(j == 2) f[j][i] += (A[i] + 1) % 2;
			if(j == 3) f[j][i] += A[i] ? A[i] % 2 : 2;
			if(j == 4) f[j][i] += A[i];
		}
	}
	LL ans = 1E18;
	for(int j = 0; j < 5; j += 1) ans = min(ans, f[j][N]);
	cout << ans;
}
### Prompt

Generate 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>
typedef long long LL;
using namespace std;
auto no = [](){cout << "NO"; exit(0);};
auto read = [](){int x; cin >> x; return x;};
#define maxn 240000
LL A[maxn];
LL f[5][maxn];
int main(){
	ios::sync_with_stdio(false);
	int N;
	cin >> N;
	for(int i = 1; i <= N; i += 1) cin >> A[i];
	for(int i = 1; i <= N; i += 1){
		LL m = 1E18;
		for(int j = 0; j < 5; j += 1){
			m = min(f[j][i - 1], m);
			f[j][i] = m;
			if(j == 0) f[j][i] += A[i];
			if(j == 1) f[j][i] += A[i] ? A[i] % 2 : 2;
			if(j == 2) f[j][i] += (A[i] + 1) % 2;
			if(j == 3) f[j][i] += A[i] ? A[i] % 2 : 2;
			if(j == 4) f[j][i] += A[i];
		}
	}
	LL ans = 1E18;
	for(int j = 0; j < 5; j += 1) ans = min(ans, f[j][N]);
	cout << ans;
}
```