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
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

"""
0,0,0,...,0,ev,ev,ev,,,ev,od,od,,,od,ev,ev,,,,ev,0,0,0,0,0
"""

L = int(input())
A = (int(x) for x in sys.stdin.read().split())

# どの状態まで進んだかごとに、最小スコア
a,b,c,d,e = 0,0,0,0,0
for x in A:
    ev_score = 1 if x&1 else (0 if x > 0 else 2)
    od_score = 1-(x&1)
    a1 = a + x
    b1 = min(a,b) + ev_score
    c1 = min(a,b,c) + od_score
    d1 = min(c,d) + ev_score
    e1 = min(b,c,d,e) + x
    a,b,c,d,e = a1,b1,c1,d1,e1

answer = min(a,b,c,d,e)
print(answer)