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
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)
inf = 10**18

N = int(input())
A = tuple(int(input()) for _ in range(N))

"""
0: zero_L
1: even_L
2: odd
3: even_R
4: zero_R
"""
dp = [inf] * 5
for i, a in enumerate(A):
    if i == 0:
        if a == 0:
            dp[0] = a
            dp[1] = 2
            dp[2] = 1
            dp[3] = 2
            dp[4] = a
        elif a % 2 == 0:
            dp[0] = a
            dp[1] = 0
            dp[2] = 1
            dp[3] = 0
            dp[4] = a
        else:
            dp[0] = a
            dp[1] = 1
            dp[2] = 0
            dp[3] = 1
            dp[4] = a
        continue

    newDP = [inf]*5
    if a == 0:
        newDP[0] = dp[0] + a
        newDP[1] = min(dp[0], dp[1]) + 2
        newDP[2] = min(dp[0], dp[1], dp[2]) + 1
        newDP[3] = min(dp[0], dp[1], dp[2], dp[3]) + 2
        newDP[4] = min(dp[0], dp[1], dp[2], dp[3], dp[4]) + a
    elif a % 2 == 1:
        newDP[0] = dp[0] + a
        newDP[1] = min(dp[0], dp[1]) + 1
        newDP[2] = min(dp[0], dp[1], dp[2])
        newDP[3] = min(dp[0], dp[1], dp[2], dp[3]) + 1
        newDP[4] = min(dp[0], dp[1], dp[2], dp[3], dp[4]) + a
    else:
        newDP[0] = dp[0] + a
        newDP[1] = min(dp[0], dp[1])
        newDP[2] = min(dp[0], dp[1], dp[2]) + 1
        newDP[3] = min(dp[0], dp[1], dp[2], dp[3])
        newDP[4] = min(dp[0], dp[1], dp[2], dp[3], dp[4]) + a
    dp = newDP

print(min(dp))