using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
//using Edge = Pair<long, int>;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
        //WriteLine(Solve());
    }
    static void Solve()
    {
        var num = Input.num;
        var ps = Input.ar1D(num);
        var uf = new UnionFind(num + 1);
        var bo = new bool[num + 1];
        for(var i = 0; i < num; i++)
        {
            bo[ps[i]] = true;
            if (bo[ps[i] - 1])
                uf.Union(ps[i], ps[i] - 1);
        }
        var m = 0;
        for (var i = 1; i <= num; i++)
            m = Max(m, uf.Size(i));
        WriteLine(num - m);
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static char[][] gred(int h)
        => Enumerable.Repeat(0, h).Select(_ => read.ToCharArray()).ToArray();
    public static int[] ar1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => num).ToArray();
    public static long[] arL1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => numL).ToArray();
    public static string[] strs(int n)
        => Enumerable.Repeat(0, n).Select(_ => read).ToArray();
    public static int[][] ar2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => ar).ToArray();
    public static long[][] arL2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => arL).ToArray();
    public static T getValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        return default(T);
    }
    public static string[] Make<T1, T2>(out T1 v1, out T2 v2)
    {
        var r = read.Split(' ');
        v1 = getValue<T1>(r[0]);
        v2 = getValue<T2>(r[1]);
        return r;
    }
    public static string[] Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        var r = Make(out v1, out v2);
        v3 = getValue<T3>(r[2]);
        return r;
    }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public const int MOD = 1000000007;
}

public class UnionFind
{
    private int _num;
    private int[] _parent, _size, _rank;
    public UnionFind(int num)
    {
        _num = num;
        _parent = new int[num];_size = new int[num];_rank = new int[num];
        for(var i = 0; i < num; i++) { _parent[i] = i;_size[i] = 1;}
    }
    private int Find(int i)
        => i == _parent[i] ? i : (_parent[i] = Find(_parent[i]));
    public int Parent(int i)
        => Find(i);
    public int Size(int i)
        => _size[Find(i)];
    public bool Union(int v1,int v2)
    {
        v1 = Find(v1);v2 = Find(v2);
        if (v1==v2) return false;
        _num--;
        if (_rank[v1] > _rank[v2])
        {
            _parent[v2] = v1;
            _size[v1] += _size[v2];
        }
        else
        {
            _parent[v1] = v2;
            _size[v2] += _size[v1];
            if (_rank[v1] == _rank[v2])
                _rank[v2]++;
        }
        return true;
    }
    public bool IsSame(int v1, int v2)
        => Find(v1) == Find(v2);
}

Measured memory_bytes: 20444