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 = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


l = int(input())
a = [None]*l
for i in range(l):
    a[i] = int(input())
dp = [[float("inf")]*(l+1) for _ in range(5)]
for i in range(5):
    dp[i][0] = 0
def c1(v):
    if v==0:
        return 2
    else:
        return v%2
def c2(v):
    if v%2==0:
        return 1
    else:
        return 0
for i in range(1,l+1):
    v = a[i-1]
    m = dp[0][i-1]
    dp[0][i] = m + v
    m = min(m, dp[1][i-1])
    dp[1][i] = m + c1(v)
    m = min(m, dp[2][i-1])
    dp[2][i] = m + c2(v)
    m = min(m, dp[3][i-1])
    dp[3][i] = m + c1(v)
    m = min(m, dp[4][i-1])
    dp[4][i] = m + v
ans = min(dp[i][l] for i in range(5))
print(ans)