using System;
using System.IO;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Contest.D
{
	static class Program
	{
		public static void Main(string[] args)
		{
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);

			Scanner cin = new Scanner();

			int n = cin.NextInt();
			var a = new List<Pair<int, int>>();
			for (int i = 0; i < n; i++)
			{
				int x = cin.NextInt();
				a.Add(new Pair<int, int>(x, i));
			}
			a.Sort();
			int maxascend = 1;
			int now = 1;
			int prev = a[0].second;
			for (int i = 1; i < n; i++)
			{
				if (a[i].second > prev) now++;
				else
				{
					maxascend = Math.Max(now, maxascend);
					now = 1;
				}
				prev = a[i].second;
			}
			maxascend = Math.Max(now, maxascend);

			Console.WriteLine(n - maxascend);

			Console.Out.Flush();
		}
	}
	public class Pair<T, U> : IComparable, IEquatable<Pair<T, U>> where T : IComparable<T>, IEquatable<T> where U : IComparable<U>, IEquatable<U>
	{
		public T first;
		public U second;

		public Pair(T first, U second)
		{
			this.first = first;
			this.second = second;
		}

		public int CompareTo(object obj)
		{
			Pair<T, U> castedObj = (Pair<T, U>)obj;
			int x = first.CompareTo(castedObj.first);
			if (x != 0) return x;
			else return second.CompareTo(castedObj.second);
		}

		public static bool operator ==(Pair<T, U> x, Pair<T, U> y) => x.CompareTo(y) == 0;

		public static bool operator !=(Pair<T, U> x, Pair<T, U> y) => x.CompareTo(y) != 0;

		public static bool operator <(Pair<T, U> x, Pair<T, U> y) => x.CompareTo(y) == 1;

		public static bool operator >(Pair<T, U> x, Pair<T, U> y) => x.CompareTo(y) == -1;

		public static bool operator <=(Pair<T, U> x, Pair<T, U> y) => x.CompareTo(y) > 0;

		public static bool operator >=(Pair<T, U> x, Pair<T, U> y) => x.CompareTo(y) < 0;

		public bool Equals(Pair<T, U> x) => first.Equals(x.first) && second.Equals(x.second);

		/*public override bool Equals(object obj)
		{
			return obj is Pair<T, U> pair &&
				   EqualityComparer<T>.Default.Equals(first, pair.first) &&
				   EqualityComparer<U>.Default.Equals(second, pair.second);
		}

		public override int GetHashCode()
		{
			unchecked
			{
				var hashCode = 405212230;
				hashCode = hashCode * -1521134295 + EqualityComparer<T>.Default.GetHashCode(first);
				hashCode = hashCode * -1521134295 + EqualityComparer<U>.Default.GetHashCode(second);
				return hashCode;
			}
		}*/
	}

	class Scanner
	{
		string[] s;
		int i;

		char[] cs = new char[] { ' ' };

		public Scanner()
		{
			s = new string[0];
			i = 0;
		}

		public string Next()
		{
			if (i < s.Length) return s[i++];
			string st = Console.ReadLine();
			while (st == "") st = Console.ReadLine();
			s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
			if (s.Length == 0) return Next();
			i = 0;
			return s[i++];
		}

		public int NextInt()
		{
			return int.Parse(Next());
		}

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = NextInt() + add;
			}
			return Array;
		}

		public long NextLong()
		{
			return long.Parse(Next());
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = NextLong() + add;
			}
			return Array;
		}

		public double NextDouble()
		{
			return double.Parse(Next());
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = NextDouble() + add;
			}
			return Array;
		}
	}
}

Measured memory_bytes: 27204