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: Wrong Answer)

using System;
using System.Linq;
using System.Diagnostics;
using System.Collections.Generic;
using static System.Math;

class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] p = Enumerable.Repeat(0, n).Select(_ => int.Parse(Console.ReadLine())).ToArray();
        //ある中心から順々に下ってる場合は嬉しい
        //中心の数字を決めます
        //中心の数字から上が全て順、または下が全て順であれば、逆側をもう一度やり直すだけ
        //それより上が順だったら?一番上を中心にすればいいだけ
        //昇順の最大まで求める
        int next = 1;
        for (int i = 0; i < p.Length; i++)
        {
            if (p[i] == next) next++;
        }
        int upperLim = next - 1;
        next = n;
        for (int i = p.Length - 1; i >= 0; i--)
        {
            if (p[i] == next) next--;
        }
        int lowerLim = next + 1;
        Console.WriteLine(n - Max(upperLim, n - lowerLim + 1));
    }
}