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.readline

N = int(input())
A = [int(input()) for _ in range(N)]

p1 = 0
p2 = 0
P1 = [0]
P2 = [0]
for a in A:
    if a == 0:
        p1 -= 2
        p2 += 1
    elif a % 2 == 0:
        p2 -= 1
    elif a % 2 == 1:
        p1 -= 1
        p2 += 1
    p1 += a
    P1.append(p1)
    P2.append(p2)

S = sum(A)
dp = [[0, 0, 0, 0] for _ in range(N+1)]

dp[N] = [P1[N], P1[N]+P2[N], -P1[N], 0]

for i in reversed(range(N)):
    dp[i][0] = max(dp[i+1][0], P1[i])
    dp[i][1] = max(dp[i+1][1], P2[i]+dp[i][0])
    dp[i][2] = min(dp[i+1][2], P2[i]-dp[i][1])
    dp[i][3] = min(dp[i+1][3], P1[i]+dp[i][2])

print(dp[0][3]+S)   
