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-mcs 6.8.0.105) (judge verdict: Accepted)

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

class Program
{
	//Main
	static void Main(string[] args)
	{
		//読み込む
		string S = Console.ReadLine();
		int N = int.Parse(S);

		int[] Pn = new int[N];
		for(int i=0; i<N; i++){
			//インデックスがややこしくならないように、最初から-1しておく
			int p = int.Parse(Console.ReadLine()) - 1;
			Pn[i] = p;
		}

		//数列Qnを作成
		/*
		各インデックスiについて、Pnでiが何番目に位置していたかを示す数列
		e.g. Qn[3] = 6のとき、
		Pnでは、3という数字は6番目に位置していた
		（即ち、Pn[6] = 3だった）
		*/
		int[] Qn = new int[N];
		for(int i=0; i<N; i++){
			Qn[Pn[i]] = i;
		}

		//Qnの中で、連続して単調増加しているうち最長の部分を求めれば良い
		/*
		cf. LSIとは違い、増加部分が連続（数列内で隣接）している必要あり
		*/
		int max = 1;
		int cnt = 1;
		for(int i=1; i<N; i++){
			//連続部分が単調増加の場合
			if(Qn[i] > Qn[i-1]){
				cnt ++;
			}
			//そうではない場合
			else{
				if(cnt > max){
					max = cnt;
				}
				//初期化
				cnt = 1;
			}
		}
		//最後まで増加した場合、改めてmaxの更新を確認する必要あり
		if(cnt > max){
			max = cnt;
		}

		int ans = N - max;

		Console.WriteLine(ans);
	}
}