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

INF = int(1e15)
DP = [[INF] * (n+1) for i in range(5)]
for i in range(4):
    DP[i][0] = 0

for i in range(n):
    DP[0][i+1] = DP[0][i] + A[i]
    DP[1][i+1] = min(DP[j][i] for j in range(2)) + (A[i] % 2 if A[i] != 0 else 2)
    DP[2][i+1] = min(DP[j][i] for j in range(3)) + (A[i] + 1) % 2
    DP[3][i+1] = min(DP[j][i] for j in range(4)) + (A[i] % 2 if A[i] != 0 else 2)
    DP[4][i+1] = min(DP[j][i] for j in range(1, 5)) + A[i]

print(min(DP[i][n] for i in range(1, 5)))