Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

4
1
0
2
3

Sample Output 1

1

Assume that Snuke walks as follows:

He starts walking at coordinate 3 and finishes walking at coordinate 4, visiting coordinates 3,4,3,2,3,4 in this order.

Then, Snuke's four ears will contain 0,0,2,3 stones, respectively.
Ringo can satisfy the requirement by putting one stone in the first ear.

Sample Input 2

8
2
0
0
2
1
3
4
1

Sample Output 2

3

Sample Input 3

7
314159265
358979323
846264338
327950288
419716939
937510582
0

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Runtime.CompilerServices;

namespace MinPro2019D
{
    public class Program
    {
        void Solve(SimpleScanner ss, StreamWriter sw)
        {
            //---------------------------------
            var L = ss.NextLong();
            var dp = new long[5];

            for (var i = 0; i < L; i++)
            {
                var A = ss.NextLong();
                var x = A == 0 ? 2 : A & 1;

                dp[0] += A;
                dp[1] += x;
                dp[2] += (x & 1) ^ 1;
                dp[3] += x;
                dp[4] += A;

                for (var t = 1; t < 5; t++)
                {
                    dp[t] = Math.Min(dp[t], dp[t - 1]);
                }
            }

            sw.WriteLine(dp[4]);
            //---------------------------------
        }

        static void Main()
        {
            var ss = new SimpleScanner(Console.OpenStandardInput());
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            new Program().Solve(ss, sw);
            sw.Flush();
        }
    }

    public class SimpleScanner
    {
        const int DefaultCapacity = 4096;

        readonly Stream stream;
        readonly int capacity;
        readonly byte[] buffer;
        readonly List<char> chars;

        int index;
        int length;
        bool isEof;

        public SimpleScanner(Stream stream, int capacity = DefaultCapacity)
        {
            this.stream = stream;
            this.capacity = capacity;
            this.buffer = new byte[capacity];
            this.chars = new List<char>();

            Reload();
        }

        void Reload()
        {
            index = 0;
            length = stream.Read(buffer, 0, capacity);
            isEof = length == 0;
            if (isEof) buffer[0] = 0;
        }

        byte Peek()
        {
            return buffer[index];
        }

        byte Read()
        {
            var ret = Peek();
            if (++index >= length) Reload();
            return ret;
        }

        bool CanInput()
        {
            return 33 <= Peek() && Peek() <= 126;
        }

        bool IsNumber()
        {
            return 48 <= Peek() && Peek() <= 57;
        }

        public string Next()
        {
            if (isEof) throw new EndOfStreamException();

            chars.Clear();
            while (!CanInput()) Read();
            while (CanInput()) chars.Add((char)Read());
            return new string(chars.ToArray());
        }

        public int NextInt()
        {
            if (isEof) throw new EndOfStreamException();

            return (int)NextLong();
        }

        public long NextLong()
        {
            if (isEof) throw new EndOfStreamException();

            var ret = 0L;
            var isNegative = false;

            while (!IsNumber()) isNegative = Read() == 45;
            while (IsNumber()) ret = ret * 10 + Read() - 48;
            return isNegative ? -ret : ret;
        }

        public double NextDouble()
        {
            if (isEof) throw new EndOfStreamException();

            var integerPart = NextLong();
            if (Peek() == 46) Read();

            double decimalPart = 0.0, place = 1.0;
            while (IsNumber()) decimalPart += (Read() - 48) * (place /= 10.0);
            return integerPart + (integerPart < 0 ? -decimalPart : decimalPart);
        }
    }
}