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
import sys
input = sys.stdin.readline

def main():
  l = int(input())
  dp = [[float('inf') for _ in range(l+1)] for _ in range(5)]
  dp[0][0] = 0
  for i in range(l):
    a = int(input())
    for j in range(5):
      for k in range(j, 5):
        cost = a
        if k == 1 or k == 3:
          if a % 2 == 0 and a > 0:
            cost = 0
          elif a > 0:
            cost = 1
          else:
            cost = 2
        elif k == 2:
          if a % 2 == 1:
            cost = 0
          else:
            cost = 1
        if dp[k][i+1] > dp[j][i] + cost:
          dp[k][i+1] = dp[j][i] + cost
  print(min([dpp[-1] for dpp in dp]))


if __name__ == '__main__':
  main()
