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 System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;
//using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;


    void solve()
    {
        int N = cin.nextint;
        var C = new int[N];

        var J = new bool[N];
        var A = new int[N + 1];
        var B = new int[N];


        for (int i = 0; i < N; i++)
        {
            C[i] = cin.nextint;
            A[C[i]] = A[C[i] - 1] + 1;
        }

        //WriteLine(string.Join(" ", A));

        WriteLine(N - A.Max());


        //var X = lis(C);
        //Array.Reverse(C);
        //var Y = lis(C);

        //WriteLine(X + " " + Y);


        //WriteLine(N - lis(C));
    }

    int lis(int[] A)
    {
        var dp = new int[A.Length];
        for (int i = 0; i < A.Length; i++)
        {
            dp[i] = int.MaxValue;
        }
        foreach (var i in A)
        {
            dp[lower_bound(dp, i)] = i;
        }

        return lower_bound(dp, int.MaxValue);
    }
    int lower_bound(int[] arr, int val)
    {
        int low = 0, high = arr.Count();
        int mid;

        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid] < val) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}