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())

inf = float('inf')
dp = [[inf] * 5 for _ in range(L+1)]
dp[0][0] = 0
for i in range(1, L+1):
    a = int(input())

    b = a & 1
    c = b ^ 1
    p, n = dp[i-1], dp[i]
    n[0] = p[0] + a
    n[1] = min(p[:2]) + b
    n[2] = min(p[:3]) + c
    n[3] = min(p[:4]) + b
    n[4] = min(p[:5]) + a

    if a == 0:
        n[1] += 2
        n[3] += 2

print(min(dp[L]))