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)]
if L == 1:
    print(0)
    exit()

#累積和
rightsum = [0]*(L+1)
leftsum = [0]*(L+1)
for i in range(1,L+1):
    rightsum[i] = rightsum[i-1]+a[i-1]
    leftsum[i] = leftsum[i-1]+a[L-i]

#Re:戻ってくる Go:戻ってこなくてもよい
Reright = [0]
Goright = [0]
for i in range(L):
    if a[i] == 0:
        Goright.append(min(rightsum[i+1],1+min(Goright[-1],Reright[-1])))
        Reright.append(min(rightsum[i+1],2+Reright[-1]))
    else:
        Goright.append(min(rightsum[i+1],(a[i]+1)%2+min(Goright[-1],Reright[-1])))
        Reright.append(min(rightsum[i+1],a[i]%2+Reright[-1]))
        
Releft = [0]
Goleft = [0]
for i in range(L):
    if a[L-1-i]==0:
        Releft.append(min(leftsum[i+1],2+Releft[-1]))
        Goleft.append(min(leftsum[i+1],1+min(Goleft[-1],Releft[-1])))
    else:
        Goleft.append(min(leftsum[i+1],(a[L-1-i]+1)%2+min(Goleft[-1],Releft[-1])))
        Releft.append(min(leftsum[i+1],a[L-1-i]%2+Releft[-1]))
        
#候補cand
cand = []
for i in range(L+1):
    p1 = Reright[i]
    p2 = min(Reright[i],Goright[i])
    q1 = Releft[L-i]
    q2 = min(Releft[L-i],Goleft[L-i])
    cand.append(min(p1+q2,p2+q1))
    
print(min(cand))
    