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>
#define REP(i, a, n) for (ll i = ((ll) a); i < ((ll) n); i++)
using namespace std;
typedef long long ll;

const ll INF = 1LL << 60;
ll N, A[200000];

ll cost(ll a, ll k) {
  if (k == 0 || k == 4) {
    return a;
  } else if (k == 1 || k == 3) {
    return a < 2 ? 2 - a : a % 2;
  } else {
    return a < 1 ? 1 - a : (a + 1) % 2;
  }
}

int main(void) {
  cin >> N;
  REP(i, 0, N) cin >> A[i];

  vector<vector<ll>> dp(N + 1, vector<ll>(5, INF));
  REP(i, 0, 5) dp[0][i] = 0;

  REP(i, 0, N) {
    REP(j, 0, 5) {
      REP(k, 0, j + 1) {
        dp[i + 1][j] = min(dp[i + 1][j], dp[i][k] + cost(A[i], j));
      }
    }
  }

  ll ans = INF;
  REP(i, 0, 5) ans = min(ans, dp[N][i]);
  cout << ans << endl;
}