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
l = int(input())
a = [int(input()) for _ in range(l)]
a.insert(0, 0)
dp = [[1000000] * (l + 1) for _ in range(4)]
for i in range(4):
    dp[i][0] = 0
for i in range(1, l + 1):
    dp[0][i] = dp[0][i - 1] + a[i]
for i in range(1, 4):
    for j in range(1, l + 1):
        if i == 2:
            x = abs(a[j] % 2 - 1)
        else:
            x = abs(2 - min(a[j] % 2 + 2, a[j]))
        dp[i][j] = min(dp[i - 1][j], dp[i][j - 1] + x)
ans = dp[3][l]
s = 0
for i in range(l - 1, -1, -1):
    s += a[i + 1]
    ans = min(ans, dp[3][i] + s)
print(ans)