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
#https://atcoder.jp/contests/yahoo-procon2019-qual/tasks/yahoo_procon2019_qual_d
#2019-02-10

#DP

L = int(input())
A = [int(input()) for i in range(L)]

DP = [0 for i in range(5)]

def cost(s, a):
    if s == 0 or s == 4:
        return a
    elif s == 1 or s == 3:
        if a > 0:
            return a%2
        else:
            return 2
    else:
        return (a+1)%2

for i in range(L):
    n = [min(DP[:i+1]) for i in range(5)]
    a = A[i]
    DP[0] = n[0] + cost(0, a)
    DP[1] = n[1] + cost(1, a)
    DP[2] = n[2] + cost(2, a)
    DP[3] = n[3] + cost(3, a)
    DP[4] = n[4] + cost(4, a)



print(min(DP))