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
import math
input = sys.stdin.readline
MOD = 10**9 + 7

n = int(input())
a = []
for i in range(n):
    a.append(int(input()))

# dp[i][j], i:processed i-th item, j:status
dp = [[n] * (n + 1) for _ in range(5)]
for i in range(5):
    dp[i][0] = 0
for i, item in enumerate(a):
    if item != 0:
        odd_cost = (item % 2 == 1)
        even_cost = (item % 2 == 0)
        # from 0 
        dp[0][i+1] = min(dp[0][i+1], dp[0][i] + item)
        dp[1][i+1] = min(dp[1][i+1], dp[0][i] + odd_cost)
        dp[2][i+1] = min(dp[2][i+1], dp[0][i] + even_cost)
        dp[3][i+1] = min(dp[3][i+1], dp[0][i] + odd_cost)
        dp[4][i+1] = min(dp[4][i+1], dp[0][i] + item)
        # from 1
        dp[1][i+1] = min(dp[1][i+1], dp[1][i] + odd_cost)
        dp[2][i+1] = min(dp[2][i+1], dp[1][i] + even_cost)
        dp[3][i+1] = min(dp[3][i+1], dp[1][i] + odd_cost)
        dp[4][i+1] = min(dp[4][i+1], dp[1][i] + item)
        # from 2
        dp[2][i+1] = min(dp[2][i+1], dp[2][i] + even_cost)
        dp[3][i+1] = min(dp[3][i+1], dp[2][i] + odd_cost)
        dp[4][i+1] = min(dp[4][i+1], dp[2][i] + item)
        # from 3
        dp[3][i+1] = min(dp[3][i+1], dp[3][i] + odd_cost)
        dp[4][i+1] = min(dp[4][i+1], dp[3][i] + item)
        # from 4
        dp[4][i+1] = min(dp[4][i+1], dp[4][i] + item)
    else:
        # from 0 
        dp[0][i+1] = min(dp[0][i+1], dp[0][i])
        dp[1][i+1] = min(dp[1][i+1], dp[0][i] + 2)
        dp[2][i+1] = min(dp[2][i+1], dp[0][i] + 1)
        dp[3][i+1] = min(dp[3][i+1], dp[0][i] + 2)
        dp[4][i+1] = min(dp[4][i+1], dp[0][i])
        # from 1
        dp[1][i+1] = min(dp[1][i+1], dp[1][i] + 2)
        dp[2][i+1] = min(dp[2][i+1], dp[1][i] + 1)
        dp[3][i+1] = min(dp[3][i+1], dp[1][i] + 2)
        dp[4][i+1] = min(dp[4][i+1], dp[1][i])
        # from 2
        dp[2][i+1] = min(dp[2][i+1], dp[2][i] + 1)
        dp[3][i+1] = min(dp[3][i+1], dp[2][i] + 2)
        dp[4][i+1] = min(dp[4][i+1], dp[2][i])
        # from 3
        dp[3][i+1] = min(dp[3][i+1], dp[3][i] + 2)
        dp[4][i+1] = min(dp[4][i+1], dp[3][i])
        # from 4
        dp[4][i+1] = min(dp[4][i+1], dp[4][i])

ans = n
for line in dp:
    ans = min(ans, line[n])
print(ans)