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
#ふぇー
import sys
def 解():
    L=int(input())
    aA=[int(_) for _ in sys.stdin.readlines()]
    dp = [0]*5
    for i in range(L):
        i生 = aA[i]
        bA = i生 % 2
        i偶 = (2 if i生 == 0 else bA)
        i奇 = (1 if i生 == 0 else ( 0 if bA else 1) )
        dp[4] = min(dp[:]) + i生
        dp[3] = min(dp[:4]) + i偶
        dp[2] = min(dp[:3]) + i奇
        dp[1] = min(dp[:2]) + i偶
        dp[0] = dp[0] + i生
    print(min(dp))
解()
