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
def main():
    from itertools import accumulate as ac
    n = int(input())
    a = [int(input()) for _ in [0]*n]
    a_ac = [0]+list(ac(a))
    s = a_ac[-1]

    dp0 = [0]*(n+1)
    dp1 = [0]*(n+1)
    dp2 = [0]*(n+1)
    dp3 = [0]*(n+1)

    for i in range(1, n+1):
        p = dp0[i-1]
        q = dp1[i-1]
        ai = a[i-1]
        dp0[i] = min(p+((ai+1) % 2), q+(ai % 2 if ai > 0 else 2), a_ac[i])
        dp1[i] = min(q+(ai % 2 if ai > 0 else 2), a_ac[i])

    for i in range(n-1, -1, -1):
        p = dp2[i+1]
        q = dp3[i+1]
        ai = a[i]
        dp2[i] = min(p+((ai+1) % 2), q+(ai % 2 if ai > 0 else 2), s-a_ac[i])
        dp3[i] = min(q+(ai % 2 if ai > 0 else 2), s-a_ac[i])

    dp_l = [min(i, j) for i, j in zip(dp0, dp1)]
    dp_r = [min(i, j) for i, j in zip(dp2, dp3)]
    print(min([i+j for i, j in zip(dp_l, dp_r)]))


main()
