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
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

def main():
    n=II()
    inf=10**16
    aa=[II() for _ in range(n)]

    dpl=[inf]*(n+1)
    dpl[0]=0
    s=0
    for i in range(n):
        a=aa[i]
        s+=a
        dpl[i+1]=s
        if a==0:dpl[i+1]=min(dpl[i+1],dpl[i]+2)
        else:dpl[i+1]=min(dpl[i+1],dpl[i]+a%2)
    #print(dpl)

    dpr=[inf]*(n+1)
    dpr[n]=0
    s=0
    for i in range(n-1,-1,-1):
        a=aa[i]
        s+=a
        dpr[i]=s
        if a==0:dpr[i]=min(dpr[i],dpr[i+1]+2)
        else:dpr[i]=min(dpr[i],dpr[i+1]+a%2)
    #print(dpr)

    even=[0]
    for a in aa:
        if a%2:even.append(even[-1])
        else:even.append(even[-1]+1)
    #print(even)

    mn=inf
    ans=inf
    for i in range(n+1):
        mn=min(mn,dpl[i]-even[i])
        cur=mn+dpr[i]+even[i]
        ans=min(ans,cur)
    #print(aa)
    print(ans)

main()