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;
#define ll long long
#define f(i, x, n) for(int i = x; i < (int)(n); ++i)

int const N = 200000;
ll const inf = 1e18;
int x[N + 1];
ll dp[N + 1][5];

int main(){
	int n;
	scanf("%d", &n);
	f(i, 1, n + 1)scanf("%d", x + i);
	f(i, 0, n + 1)f(j, 0, 5)dp[i][j] = inf;
	dp[0][0] = 0;
	f(i, 1, n + 1)f(j, 0, 5)if (dp[i - 1][j] < inf)f(k, j, 5){
		ll nc = dp[i - 1][j];
		if (k == 0 || k == 4)nc += x[i];
		else if (k == 1 || k == 3){
			if (x[i] == 0)nc += 2;
			else if (x[i] & 1)++nc;
		}else if (!(x[i] & 1))++nc;
		dp[i][k] = min(dp[i][k], nc);
	}
	ll an = inf;
	f(i, 0, 5)an = min(an, dp[n][i]);
	printf("%lld\n", an);
}