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 i in range(L)]
su=sum(A)
#print(A)

DP=[[0 for i in range(5)] for j in range(L+1)]

mod=A[0]%2
if A[0]==0 :
    mod=2
DP[1]=[A[0],min(A[0],mod%2),min(A[0],mod%2,(mod+1)%2),min(A[0],mod%2,(mod+1)%2),min(A[0],mod%2,(mod+1)%2)]

for i in range(2,L+1):
    mod=A[i-1]%2
    if A[i-1]==0 :
        mod=2
    DP[i][0]+=DP[i-1][0]+A[i-1]
    DP[i][1]+=min(DP[i-1][0],DP[i-1][1])+mod
    DP[i][2]+=min(DP[i-1][j] for j in range(3))+(mod+1)%2
    DP[i][3]+=min(DP[i-1][j] for j in range(4))+mod
    DP[i][4]+=min(DP[i-1][j] for j in range(5))+A[i-1]

#print(DP)
print(min(DP[L]))
