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 sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

l = int(readline())
a = list(map(int,read().split()))

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

for i in range(l):
    dp[0][i+1] = dp[0][i] + a[i]

for i in range(l):
    dp[1][i+1] = min(dp[0][i+1],
                    min(dp[0][i], dp[1][i]) + (a[i]%2 if a[i]!=0 else 2))

for i in range(l):
    dp[2][i+1] = min(dp[1][i+1],
                    min(dp[0][i], dp[1][i], dp[2][i]) + (a[i]-1)%2)

for i in range(l):
    dp[3][i+1] = min(dp[2][i+1],
                    min(dp[0][i], dp[1][i], dp[2][i], dp[3][i]) + (a[i]%2 if a[i]!=0 else 2))

for i in range(l):
    dp[4][i+1] = min(dp[3][i+1],
                    min(dp[0][i], dp[1][i], dp[2][i], dp[3][i], dp[4][i]) + a[i])

print(dp[-1][-1])