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
# -*- coding: utf-8 -*-
l = int(input())
al = [int(input()) for _ in range(l)]
INF = 10**15
dp = [INF]*5  # 0,偶数,奇数,偶数,0の状態
dp[0] = 0

def cost(i, k):
    # i番目を状態kにした時に必要な回数
    if k==0 or k==4:
        return al[i]
    elif k==1 or k==3:
        if al[i]>0:
            return al[i]%2
        else:
            return 2
    else:
        if al[i]%2==0:
            return 1
        else:
            return 0

for i in range(l):
    dp2 = [min(dp[:j+1]) for j in range(5)]
    for j in range(5):
        dp[j] = dp2[j] + cost(i,j)

    # for j in range(5):
    #     for k in range(j,5):
    #         dp[i+1][k] = min(
    #             dp[i+1][k],
    #             dp[i][j] + cost(i, k)
    #         )

print(min(dp))
