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, *A = map(int, open(0))

D = [(2, 1), (1, 0), (0, 1)]

s0 = s1 = s2 = s3 = s4 = 0

for a in A:
    e, o = D[(a - 1) % 2 + 1 if a else 0]

    s0 += a
    s1 = s0 if s0 < s1 + e else s1 + e
    s2 = s1 if s1 < s2 + o else s2 + o
    s3 = s2 if s2 < s3 + e else s3 + e
    s4 = s3 if s3 < s4 + a else s4 + a

print(min(s0, s1, s2, s3, s4))
