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
# coding: utf-8
# Your code here!
#k,a,b = [int(i) for i in input().split()]

l = int(input())
a = [int(input()) for i in [0]*l]
asum=[0]*(l+1)
for i in range(1,l+1):
    asum[i] = asum[i-1]+a[i-1]    

reven=[0]*(l+1)
leven=[0]*(l+1)
rodd=[0]*(l+1)
lodd=[0]*(l+1)

for i in range(1,l+1):
    if a[i-1] != 0:
        leven[i]=leven[i-1] + a[i-1]%2
    else:
        leven[i]=min(2+leven[i-1],asum[i])

for i in range(l-1,-1,-1):
    if a[i] != 0:
        reven[i]=reven[i+1] + a[i]%2
    else:
        reven[i]=min(2+reven[i+1],asum[l]-asum[i])

for i in range(1,l+1):
    lodd[i]=min(leven[i], lodd[i-1]+(a[i-1]+1)%2, asum[i])

for i in range(l-1,-1,-1):
    rodd[i]=min(reven[i], rodd[i+1]+(a[i]+1)%2, asum[l]-asum[i])

#print(asum)
#print(reven)
#print(leven)
#print(rodd)
#print(lodd)

ans = 5*(l+2)
for i in range(l+1):
    ans = min(ans, leven[i]+rodd[i], lodd[i]+reven[i])

print(ans)




    



