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
input = sys.stdin.readline

L=int(input())
A=[int(input()) for i in range(L)]
            
SUM=[0]
for a in A:
    SUM.append(SUM[-1]+a)

def div2(x):
    if x==0:
        return 2
    else:
        return x%2
    
DP0=[0]*(L+1)
DP1=[0]*(L+1)
DP2=[0]*(L+1)
DP3=[0]*(L+1)
DP4=[0]*(L+1)

for i in range(L):
    DP0[i]=DP0[i-1]+A[i]
    DP1[i]=min(DP0[i-1]+div2(A[i]),DP1[i-1]+div2(A[i]))
    DP2[i]=min(DP2[i-1]+(A[i]+1)%2,DP1[i-1]+(A[i]+1)%2,DP0[i-1]+(A[i]+1)%2)
    DP3[i]=min(DP3[i-1]+div2(A[i]),DP2[i-1]+div2(A[i]),DP1[i-1]+div2(A[i]),DP0[i-1]+div2(A[i]))
    DP4[i]=min(DP4[i-1]+A[i],DP3[i-1]+A[i],DP2[i-1]+A[i],DP1[i-1]+A[i],DP0[i-1]+A[i])

print(min(DP0[L-1],DP1[L-1],DP2[L-1],DP3[L-1],DP4[L-1]))
