#include <stdio.h>
typedef long long ll;

int main(void) {
  ll i, j, k, l, ans = 1e18;
  scanf("%lld", &l);
  ll dp[l][5], a[l];
  for(i = 0; i < l; ++i) scanf("%lld", &a[i]);
  for(i = 0; i < l; ++i) for(j = 0; j < 5; ++j) dp[i][j] = 1e18;
  dp[0][0] = dp[0][4] = a[0], dp[0][1] = dp[0][3] = a[0] ? a[0] % 2 : 2, dp[0][2] = a[0] % 2 ? 0 : 1;
  for(i = 1; i < l; ++i) {
    for(j = 0; j < 5; ++j) for(k = j; k < 5; ++k) {
      if(!k || k == 4) {
        if(dp[i][k] > dp[i - 1][j] + a[i]) dp[i][k] = dp[i - 1][j] + a[i];
      } else if(k == 1 || k == 3) {
        if(dp[i][k] > dp[i - 1][j] + (a[i] ? a[i] % 2 : 2)) dp[i][k] = dp[i - 1][j] + (a[i] ? a[i] % 2 : 2);
      } else {
        if(dp[i][k] > dp[i - 1][j] + (a[i] % 2 ? 0 : 1)) dp[i][k] = dp[i - 1][j] + (a[i] % 2 ? 0 : 1);
      }
    }
  }
  for(i = 0; i < 5; ++i) if(ans > dp[l - 1][i]) ans = dp[l - 1][i];
  printf("%lld", ans);
  return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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 <stdio.h>
typedef long long ll;

int main(void) {
  ll i, j, k, l, ans = 1e18;
  scanf("%lld", &l);
  ll dp[l][5], a[l];
  for(i = 0; i < l; ++i) scanf("%lld", &a[i]);
  for(i = 0; i < l; ++i) for(j = 0; j < 5; ++j) dp[i][j] = 1e18;
  dp[0][0] = dp[0][4] = a[0], dp[0][1] = dp[0][3] = a[0] ? a[0] % 2 : 2, dp[0][2] = a[0] % 2 ? 0 : 1;
  for(i = 1; i < l; ++i) {
    for(j = 0; j < 5; ++j) for(k = j; k < 5; ++k) {
      if(!k || k == 4) {
        if(dp[i][k] > dp[i - 1][j] + a[i]) dp[i][k] = dp[i - 1][j] + a[i];
      } else if(k == 1 || k == 3) {
        if(dp[i][k] > dp[i - 1][j] + (a[i] ? a[i] % 2 : 2)) dp[i][k] = dp[i - 1][j] + (a[i] ? a[i] % 2 : 2);
      } else {
        if(dp[i][k] > dp[i - 1][j] + (a[i] % 2 ? 0 : 1)) dp[i][k] = dp[i - 1][j] + (a[i] % 2 ? 0 : 1);
      }
    }
  }
  for(i = 0; i < 5; ++i) if(ans > dp[l - 1][i]) ans = dp[l - 1][i];
  printf("%lld", ans);
  return 0;
}
```