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


def calc(itr):
    dp = [0]
    turn, no_turn, no_visit = 0, 0, 0
    for a in itr:
        b = a % 2
        new_turn = min(turn, no_visit) + (2 if a == 0 else b)
        new_no_turn = min(turn, no_turn, no_visit) + (b ^ 1)
        new_no_visit = no_visit + a
        dp.append(min(new_turn, new_no_turn, new_no_visit))
        turn, no_turn, no_visit = new_turn, new_no_turn, new_no_visit
    return dp


l = int(input())
aaa = list(map(int, sys.stdin))

dp_f = calc(aaa)
dp_b = calc(reversed(aaa))
dp_b.reverse()

print(min(map(sum, zip(dp_f, dp_b))))
