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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */


import java.io.*;
import java.util.*;

/**
 *
 * @author nai
 */
public class Main
{
    public static void main(String[] args)
    {
        StringBuilder sb = new StringBuilder();
        FastScanner sc = new FastScanner(System.in);
        int N = sc.nextInt();
        int[] V = sc.nextIntArray(N);
        //1 ~ N
        int[] rV = new int[N + 1];
        for (int i = 0; i < N; i++) {
            rV[V[i]] = i;
        }
        
        int max = 1,cou = 1;
        //1 ~ N nanode
        for (int i = 2; i < N + 1; i++) {
            //dame na toki
            if(rV[i - 1] > rV[i]){
                if(max < cou){
                    max = cou;
                }
                cou = 1;
            }
            else{
                cou++;
            }
        }
        System.out.println(N - max);
        
    }
    static class FastScanner {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;
        
        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }
        
        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            
            return tokenizer.nextToken("\n");
        }
        
        public long nextLong() {
            return Long.parseLong(next());
        }
        
        public int nextInt() {
            return Integer.parseInt(next());
        }
        
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        
        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        public char[][] nextCharArray2(int h , int w){
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = next().toCharArray();
            }
            return a;
        }
        public int [][] nextIntArray2(int h, int w){
            int[][] a = new int[h][w];
            for(int hi = 0 ; hi < h ; hi++){
                for(int wi = 0 ; wi < h ; wi++){
                    a[h][w] = nextInt();
                }
            }
            return a;
        }
        
        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }
        public long [][] nextLongArray2(int h, int w){
            long[][] a = new long[h][w];
            for(int hi = 0 ; hi < h ; hi++){
                for(int wi = 0 ; wi < h ; wi++){
                    a[h][w] = nextLong();
                }
            }
            return a;
        }
    }
}