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.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;
		}
	}
}