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 rep(i,a,b) for(int i=a;i<=b;i++)
typedef long long ll;
typedef double db;
const int maxn = 5e5 + 5;
const int mod = 1e9 + 7;

ll a[maxn], dp[maxn][5];

int main(){
    int n;
    scanf("%d", &n);
    rep(i, 1, n)
        scanf("%lld", &a[i]);
    rep(i, 1, n){
        dp[i][0] = dp[i-1][0];
        rep(j, 1, 4)
            dp[i][j] = min(dp[i][j-1], dp[i-1][j]);
        dp[i][0] += a[i]; dp[i][4] += a[i];
        dp[i][1] += a[i] == 0 ? 2 : (a[i] & 1);
        dp[i][3] += a[i] == 0 ? 2 : (a[i] & 1);
        dp[i][2] += a[i] & 1 ^ 1;
    }
    ll ans = dp[n][0];
    rep(i, 1, 4)
        ans = min(ans, dp[n][i]);
    printf("%lld\n", ans);
    return 0;
}
