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
#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]; }

	array<ll, 5> now;
	now.fill(INF);
	now[0] = 0;
	for (int i = 1; i <= L; ++i) {
		ll base = INF;
		for (int j = 0; j < 5; ++j) {
			base = min(base, now[j]);
			ll add = 0;
			if ((j == 0) || (j == 4)) { add = A[i]; }
			if ((j == 1) || (j == 3)) { add = (A[i] == 0 ? 2 : A[i] % 2); }
			if (j == 2) { add = 1 - (A[i] % 2); }

			now[j] = base + add;
		}
	}

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

	return 0;
}
