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
#!/usr/bin/env python3
import sys

INF = float('inf')

def solve(n: int, A: "List[int]"):
    dp = [[INF] * 5  for _ in range(n + 1)]
    dp[0][0] = 0
    dp[0][1] = 0
    dp[0][2] = 0
    for i in range(n):
        for j in range(5):
            if j == 0 or j == 4:
                extra = A[i]
            elif j == 1 or j == 3:
                extra = A[i] % 2 if A[i] > 0 else 2
            else:
                extra = (A[i] + 1) % 2
            dp[i + 1][j] = min(dp[i + 1][j], dp[i][j] + extra)
            for k in range(j + 1, 5):
                dp[i + 1][k] = min(dp[i + 1][k], dp[i][j] + extra)
        #print(dp[i + 1])
    print(min(dp[n]))
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    L = int(next(tokens))  # type: int
    A = [ int(next(tokens)) for _ in range(L) ]  # type: "List[int]"
    solve(L, A)

if __name__ == '__main__':
    main()
