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 i in range(L)]

Asum = [0]
for i, a in enumerate(A):
    Asum.append(Asum[i] + a)

Emin = [0 for i in range(L + 1)]
Zmin = [0 for i in range(L + 1)]

for i in range(L)[:: -1]:
    a = A[i]
    if a == 0:
        Emin[i] = 2 + Emin[i + 1]
        Zmin[i] = 1 + min(Emin[i + 1], Zmin[i + 1])
    elif a % 2 == 0:
        Emin[i] = Emin[i + 1]
        Zmin[i] = 1 + min(Emin[i + 1], Zmin[i + 1])
    else:
        Emin[i] = 1 + Emin[i + 1]
        Zmin[i] = min(Emin[i + 1], Zmin[i + 1])
    Emin[i] = min(Emin[i], Asum[L] - Asum[i])
    Zmin[i] = min(Zmin[i], Asum[L] - Asum[i])


A.reverse()

Asum = [0]
for i, a in enumerate(A):
    Asum.append(Asum[i] + a)

Emin2 = [0 for i in range(L + 1)]
Zmin2 = [0 for i in range(L + 1)]

for i in range(L)[:: -1]:
    a = A[i]
    if a == 0:
        Emin2[i] = 2 + Emin2[i + 1]
        Zmin2[i] = 1 + min(Emin2[i + 1], Zmin2[i + 1])
    elif a % 2 == 0:
        Emin2[i] = Emin2[i + 1]
        Zmin2[i] = 1 + min(Emin2[i + 1], Zmin2[i + 1])
    else:
        Emin2[i] = 1 + Emin2[i + 1]
        Zmin2[i] = min(Emin2[i + 1], Zmin2[i + 1])
    Emin2[i] = min(Emin2[i], Asum[L] - Asum[i])
    Zmin2[i] = min(Zmin2[i], Asum[L] - Asum[i])

ans = 3000000
for i in range(L):
    ans = min(ans, min(Emin[i], Zmin[i]) + min(Emin2[L - i], Zmin2[L - i]))

print(ans)