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: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Collections;
import java.util.NoSuchElementException;
 
public class Main {
	private static FastScanner sc = new FastScanner();
	
	public static void main(String[] args) {
		int N = sc.nextInt();
		ArrayList<Integer> P1 = new ArrayList<>();
		ArrayList<Integer> P2 = new ArrayList<>();
		for(int i=0; i<N; i++) {
			int temp = sc.nextInt()-1;
			P1.add(temp);
			P2.add(temp);
		}
		Collections.reverse(P2);
		int i = 0;
		int num = 0;
		int seq = 0;
		int maxseq = 0;
		while(true) {
			if(i == P1.size()) {
				if(seq > maxseq) maxseq = seq;
				seq = 0;
				i = 0;
				if(P1.size() == 0) {
					break;
				}
			} else if(P1.get(i) == num) {
				num++;
				seq++;
				P1.remove(i);
			} else {
				i++;
			}
		}
		num = N - 1;
		while(true) {
			if(i == P2.size()) {
				if(seq > maxseq) maxseq = seq;
				seq = 0;
				i = 0;
				if(P2.size() == 0) {
					break;
				}
			} else if(P2.get(i) == num) {
				num--;
				seq++;
				P2.remove(i);
			} else {
				i++;
			}
		}
		System.out.println(N - maxseq);
	}
	static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if(ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch(IOException e) {
                    e.printStackTrace();
                }
                if(buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
        public boolean hasNext() { skipUnprintable(); return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}