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 _ in range(L)]

INF = 1E50
ans1 = sum(A)  # None
ans2 = ans1 - 1 if ans1 > 0 else 0

a_alpha_t = list(map(lambda x: 2 if x == 0 else x % 2, A))
a_b_t = list(map(lambda x: (x + 1) % 2, A))

total_val = 0
a_b_val = 0
a_alpha_val = 0
total = [0 for _ in range(L)]
a_b = list(total)
a_alpha = list(total)
for i in range(L):
    total_val += A[i]
    a_b_val += a_b_t[i]
    a_alpha_val += a_alpha_t[i]
    total[i] = total_val
    a_b[i] = a_b_val
    a_alpha[i] = a_alpha_val








ans = [0 for _ in range(5)]
for i, a in enumerate(A):
    tmp_ans=  [INF for _ in range(5)]
    tmp_ans[0] = total[i]
    tmp_ans[1] = min(ans[1]+a_alpha_t[i],total[i])
    tmp_ans[2]= min(tmp_ans[1],ans[2]+a_b_t[i])
    tmp_ans[3]= min(tmp_ans[2],ans[3]+a_alpha_t[i])
    tmp_ans[4] = min(tmp_ans[3],ans[4]+A[i])
    ans = tmp_ans

print(min(ans+[ans1,ans2]))