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 x in range(l)]
def ds_tu(i):
    if a[i]==0:return 2
    return a[i]%2
ans=[[0 for i in range(5)] for j in range(l)]
ans[0][0]=a[0]
ans[0][1]=ds_tu(0)
ans[0][2]=(a[0]+1)%2
ans[0][3]=ds_tu(0)
ans[0][4]=a[0]
for i in range(1,l):
    ans[i][0]=ans[i-1][0]+a[i]
    ans[i][1]=min(ans[i-1][0:2])+ds_tu(i)
    ans[i][2]=min(ans[i-1][0:3])+(a[i]+1)%2
    ans[i][3]=min(ans[i-1][0:4])+ds_tu(i)
    ans[i][4]=min(ans[i-1])+a[i]
    
print(min(ans[l-1]))
    