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, = map(int, raw_input().split())
A = [0]*L
dp = []
for i in xrange(L):
  A[i], = map(int, raw_input().split())
  dp.append([float("inf")]*5)
i=0
e = 2-A[i] if A[i]<2 else A[i]%2
o = 1 if A[i]==0 else (A[i]+1)%2
dp[0][0] = A[0]
dp[0][1] = e
dp[0][2] = o
dp[0][3] = e
dp[0][4] = A[0]
for i in xrange(1, L):
  e = 2-A[i] if A[i]<2 else A[i]%2
  o = 1 if A[i]==0 else (A[i]+1)%2
  dp[i][0] = min(dp[i-1][:1]) + A[i]
  dp[i][1] = min(dp[i-1][:2]) + e
  dp[i][2] = min(dp[i-1][:3]) + o
  dp[i][3] = min(dp[i-1][:4]) + e
  dp[i][4] = min(dp[i-1][:5]) + A[i]
print min(dp[-1])