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
# -*- coding: utf-8 -*-
import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(10000)


def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def error_mat_print(m):
    for r in m:
        print(r, file=sys.stderr)

def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


@mt
def slv(L, A):

    dp = [[sys.maxsize] * (L+1) for _ in range(6)]
    for i in range(5):
        dp[i][0] = 0
    # dp[0][0] = 0

    def s(a, t):
        if t == 0 or t == 4:
            return a
        if t == 1 or t == 3:
            if a == 0:
                return 2
            else:
                return a % 2
        else:
            return (a+1) % 2

    for i, a in enumerate(A):
        t = dp[0][i]
        dp[0][i+1] = t + a
        t = min(t, dp[1][i])
        dp[1][i+1] = t+ ((a%2) if a != 0 else 2)
        t = min(t, dp[2][i])
        dp[2][i+1] = t + ((a+1)%2)
        t = min(t, dp[3][i])
        dp[3][i+1] =t + ((a%2) if a != 0 else 2)
        t = min(t, dp[4][i])
        dp[4][i+1] = t + a

        # error_print(a)
        # error_mat_print(dp)

    return min([dp[i][L] for i in range(5)])

def main():
    L = read_int()
    A = [read_int() for _ in range(L)]
    print(slv(L, A))


if __name__ == '__main__':
    main()
