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
N=int(input())
A=[int(input()) for i in range(N)]
B=[0]*N
for i in range(N):
    if A[i]>0:
        if A[i]%2==0:
            B[i]=2
        else:
            B[i]=1
L=[0,2,1,2,0]
dp=[[10**9]*5 for i in range(N+1)]
for k in range(5):
    dp[0][k]=0
for i in range(1,N+1):
    for k in range(5):
        for k1 in range(k+1):
            if 1<=k<=3:
                dp[i][k]=min(dp[i][k],dp[i-1][k1]+abs(L[k]-B[i-1]))
            else:
                dp[i][k]=min(dp[i][k],dp[i-1][k1]+A[i-1])
ans=10**9
#print(B)
#print(dp)
for a in range(5):
    ans=min(ans,dp[N][a])
print(ans)