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
# 参考
# https://atcoder.jp/contests/yahoo-procon2019-qual/submissions/4223019

L = int(input())
a_list = [int(input()) for _ in range(L)]

dp = [[0] * 5 for _ in range(L+1)]

for i in range(L):
    a = a_list[i]

    if a > 0:
        even = a % 2
    else:
        even = 2
    odd = (a + 1) % 2

    #0
    dp[i+1][0] = dp[i][0] + a
    #偶数（0であれば0の項目に含まれるはずなので、0より大きい偶数）
    dp[i+1][1] = min(dp[i][:2]) + even
    #奇数（スタートとゴールの間の区間）
    dp[i+1][2] = min(dp[i][:3]) + odd
    #偶数（0であれば0の項目に含まれるはずなので、0より大きい偶数）
    dp[i+1][3] = min(dp[i][:4]) + even
    #0
    dp[i+1][4] = min(dp[i][:5]) + a
print(min(dp[L]))
