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
L = int(input())
A = [0] * (L + 1)
DP = [[0, 0, 0, 0, 0] for i in range(L + 1)]
for i in range(L):
  a = int(input())
  DP[i + 1][0] = DP[i][0] + a
  DP[i + 1][1] = min(min(DP[i][:2]), DP[i + 1][0]) + (a % 2 if a else 2)
  DP[i + 1][2] = min(min(DP[i][:3]), DP[i + 1][1]) + ((1 - a % 2) if a else 1)
  DP[i + 1][3] = min(min(DP[i][:4]), DP[i + 1][2]) + (a % 2 if a else 2)
  DP[i + 1][4] = min(min(DP[i]), DP[i + 1][3]) + a
print(min(DP[L]))