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
N=int(input())
A=[]
for i in range(N):
    A.append(int(input()))

dat=[A[i] for i in range(N)]
for i in range(1,N):
    dat[i]+=dat[i-1]

evenf=[0]*N
evenf[0]=A[0]%2
for i in range(1,N):
    t=A[i]%2
    if A[i]==0:
        t=2
    evenf[i]=min(evenf[i-1]+t,dat[i])

evenb=[0]*N
evenb[N-1]=A[-1]%2
for i in range(N-2,-1,-1):
    t=A[i]%2
    if A[i]==0:
        t=2
    if i!=0:
        evenb[i]=min(evenb[i+1]+t,dat[-1]-dat[i-1])
    else:
        evenb[i]=min(evenb[i+1]+t,dat[-1])

oddf=[0 for i in range(N)]
for i in range(1,N):
    t=(1+A[i])%2
    oddf[i]=min(oddf[i-1]+t,evenf[i])

ans=oddf[-1]
for i in range(N-1):
    ans=min(ans,evenb[i+1]+oddf[i])

print(ans)
