Problem:
Score : 500 points

Problem Statement

You are given a sequence (P_1,P_2,...,P_N) which is a permutation of the integers from 1 through N.
You would like to sort this sequence in ascending order by repeating the following operation:

Choose an element in the sequence and move it to the beginning or the end of the sequence.

Find the minimum number of operations required.
It can be proved that it is actually possible to sort the sequence using this operation.

Constraints

1 \leq N \leq 2\times 10^5

(P_1,P_2,...,P_N) is a permutation of (1,2,...,N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1
:
P_N

Output

Print the minimum number of operations required.

Sample Input 1

4
1
3
2
4

Sample Output 1

2

For example, the sequence can be sorted in ascending order as follows:

Move 2 to the beginning. The sequence is now (2,1,3,4).

Move 1 to the beginning. The sequence is now (1,2,3,4).

Sample Input 2

6
3
2
5
1
4
6

Sample Output 2

4

Sample Input 3

8
6
3
1
2
7
4
8
5

Sample Output 3

5

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

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoderSolve.Tool;

namespace AtCoderSolve
{
    class Solve
    {
        const int mod = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;

        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();
            int N = int.Parse(Console.ReadLine());
            List<Pair<int>> P = new List<Pair<int>>();

            for(var i = 0; i < N; i++)
            {
                P.Add(new Pair<int>(int.Parse(Console.ReadLine()), i));
            }

            P.Sort();
            long len = 1;
            long ans = N;
            for(var i = 0; i < N; i++)
            {
                if (i == 0) { continue; }
                if (P[i].index > P[i - 1].index)
                {
                    len++;
                }
                else
                {
                    ans = Min(ans, N - len);
                    len = 1;
                }
            }
            ans = Min(ans, N - len);

            Console.WriteLine(ans);


            //Console.Out.Flush();
        }


    }

    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }

    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for(var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
    }

    struct Pair<T> : IComparable<Pair<T>> where T : IComparable<T>
    {
        public T variable;
        public int index;

        public Pair(T val, int i)
        {
            variable = val;
            index = i;
        }

        public int CompareTo(Pair<T> otherPair)
        {
            return variable.CompareTo(otherPair.variable);
        }

        public int CompareIndex(Pair<T> otherPair)
        {
            return index.CompareTo(otherPair.index);
        }
    }



}