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
# https://yahoo-procon2019-qual.contest.atcoder.jp/tasks/yahoo_procon2019_qual_d

L = int(input())

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

INF = int(1e15)
dp = [[INF] * (L + 1) for _ in range(5)]

for i in range(4):
    dp[i][0] = 0

for i in range(L):
    dp[0][i + 1] = dp[0][i] + A[i]  # 全部取り除く
    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)) + (1 if A[i] % 2 == 0 else 0)
    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(5)) + A[i]  # 全部取り除く


print(min(dp[i][L] for i in range(1, 5)))
