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 os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7


def cumsum(li):
    ret = []
    sum = 0
    for i in li:
        sum += i
        ret.append(sum)
    return ret


# 解説AC
N = int(sys.stdin.readline())
A = [int(sys.stdin.readline()) for _ in range(N)]

# dp[i]: i まで見たときの答えの最小値
# dp[i][0]: どこも通ってない
# dp[i][1]: D まで通った
# dp[i][2]: S まで通った
# dp[i][3]: T まで通った
# dp[i][4]: U まで通った
dp = [[0] * 5 for _ in range(N)]
for i, a in enumerate(cumsum(A)):
    dp[i][0] = a
dp[0][1] = int((A[0] % 2 != 0) + (A[0] == 0) * 2)
dp[0][2] = int(A[0] % 2 != 1)
dp[0][3] = int((A[0] % 2 != 0) + (A[0] == 0) * 2)
dp[0][4] = A[0]

for i in range(1, N):
    dp[i][ 1] = min(dp[i - 1][ :1 + 1]) + int((A[i] % 2 != 0) + (A[i] == 0) * 2)
    dp[i][ 2] = min(dp[i - 1][ :2 + 1]) + int(A[i] % 2 != 1)
    dp[i][ 3] = min(dp[i - 1][ :3 + 1]) + int((A[i] % 2 != 0) + (A[i] == 0) * 2)
    dp[i][ 4] = min(dp[i - 1][ :4 + 1]) + A[i]
print(min(dp[-1]))
