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 _ in range(L)]
INF = 10**20
DP = [[INF for i in range(5)] for _ in range(L)]
DP[0][0] = A[0]
DP[0][1] = (2 if A[0] == 0 else 1 if A[0] % 2 == 1 else 0)
DP[0][2] = (1 if A[0] % 2 == 0 else 0)
DP[0][3] = (2 if A[0] == 0 else 1 if A[0] % 2 == 1 else 0)
DP[0][4] = A[0]

for i in range(1, L):
    a = A[i]
    DP[i][0] = DP[i-1][0] + a
    DP[i][1] = min(DP[i-1][:2]) + (2 if a == 0 else 1 if a % 2 == 1 else 0)
    DP[i][2] = min(DP[i-1][:3]) + (1 if a % 2 == 0 else 0)
    DP[i][3] = min(DP[i-1][:4]) + (2 if a == 0 else 1 if a % 2 == 1 else 0)
    DP[i][4] = min(DP[i-1]) + a

print(min(DP[L-1]))