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=[int(input()) for _ in range(l)]

def even(n):
    if n==0:
        return 2
    else:
        return n%2
def odd(n):
    return (n+1)%2

DP=[[0]*5 for _ in range(l)]
DP[0]=[A[0],even(A[0]),odd(A[0]),even(A[0]),A[0]]
for i in range(1,l):
    DP[i][0]=DP[i-1][0]+A[i]
    DP[i][1]=min(DP[i-1][:2])+even(A[i])
    DP[i][2]=min(DP[i-1][:3])+odd(A[i])
    DP[i][3]=min(DP[i-1][:4])+even(A[i])
    DP[i][4]=min(DP[i-1])+A[i]
print(min(DP[l-1]))