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
l = int(input())
a = []
for i in range(l):
  a.append(int(input()))
  
dp=[[0]*5 for i in range(l+1)]

for i in range(0,l):
  if a[i]==0:
    even=2
  else:
    even=a[i]%2
  
  dp[i+1][0]=dp[i][0]+a[i]
  dp[i+1][1]=min(dp[i][0],dp[i][1]) + even
  dp[i+1][2]=min(dp[i][0],dp[i][1],dp[i][2]) + (a[i]+1)%2
  dp[i+1][3]=min(dp[i][0],dp[i][1],dp[i][2],dp[i][3]) + even
  dp[i+1][4]=min(dp[i][0],dp[i][1],dp[i][2],dp[i][3],dp[i][4]) + a[i]
  
print(min(dp[l]))
  