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
# coding: utf-8

"""

o 999
o 2 3
x 2 0 2
o 2 1 2
x 2 1 2 1
o 2 1 3 1
o 2 1 3 2
o 3 1 3
x 3 2 3
o 3 2 2

- 0は両端のみ
- 偶奇の切り替わりが2回以下

0 zzoo
1 zzee
2 zzooee
3 zzeeoo
4 zzeeooee
5 zz
6 ???zz
"""

L = input()
A = [input() for _ in range(L)]

T = [L,L,L,L,L,0,L]
for a in A:
  P = T
  o = 1-a%2
  e = 1-o
  if a==0:
    e = 2
  T = [
    min(P[0]+o, P[5]+o),
    min(P[1]+e, P[5]+e),
    min(P[2]+e, P[0]+e),
    min(P[3]+o, P[1]+o),
    min(P[4]+e, P[3]+e),
    P[5]+a,
    min(P)+a,
  ]
  #print a, T
print min(T)

