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 = []
for i in range(0, l):
    a.append(int(input()))

left = [0] * (l + 1)
start= [0] * (l + 1)
goal = [0] * (l + 1)
right = [0] * (l + 1)
last = [0] * (l + 1)

for i in range(1, l + 1):
    left[i] = left[i - 1] + a[i - 1]
    
for i in range(1, l + 1):
    c = 0
    if a[i - 1] == 0:
        c = 2
    elif a[i - 1] % 2 == 1:
        c = 1
    start[i] = min(left[i], start[i - 1] + c)

for i in range(1, l + 1):
    c = 0
    if a[i - 1] % 2 == 0:
        c = 1
    goal[i] = min(start[i], goal[i - 1] + c)
    
for i in range(1, l + 1):
    c = 0
    if a[i - 1] == 0:
        c = 2
    elif a[i - 1] % 2 == 1:
        c = 1
    right[i] = min(goal[i], right[i - 1] + c)
    
for i in range(1, l + 1):
    last[i] = min(last[i - 1] + a[i - 1], right[i])
    
print(last[-1])