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
#https://atcoder.jp/contests/yahoo-procon2019-qual/tasks/yahoo_procon2019_qual_d
#2019-02-11

#DP

L = int(input())

DP = [0 for i in range(5)]

def cost(a):
    if a:
        return [a, a%2, (a+1)%2, a%2, a]
    else:
        return [0, 2, 1, 2, 0]

def list_add(in1, in2):
    return [a + b for a, b in zip(in1, in2)]

for i in range(L):
    n = [min(DP[:i+1]) for i in range(5)]
    a = int(input())
    cos = cost(a)
    DP = list_add(n, cos)



print(min(DP))