Problem:
Score : 400 points

Problem Statement

We have N bricks arranged in a row from left to right.

The i-th brick from the left (1 \leq i \leq N) has an integer a_i written on it.

Among them, you can break at most N-1 bricks of your choice.

Let us say there are K bricks remaining. Snuke will be satisfied if, for each integer i (1 \leq i \leq K), the i-th of those brick from the left has the integer i written on it.

Find the minimum number of bricks you need to break to satisfy Snuke's desire. If his desire is unsatisfiable, print -1 instead.

Constraints

All values in input are integers.

1 \leq N \leq 200000

1 \leq a_i \leq N

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum number of bricks that need to be broken to satisfy Snuke's desire, or print -1 if his desire is unsatisfiable.

Sample Input 1

3
2 1 2

Sample Output 1

1

If we break the leftmost brick, the remaining bricks have integers 1 and 2 written on them from left to right, in which case Snuke will be satisfied.

Sample Input 2

3
2 2 2

Sample Output 2

-1

In this case, there is no way to break some of the bricks to satisfy Snuke's desire.

Sample Input 3

10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

7

Sample Input 4

1
1

Sample Output 4

0

There may be no need to break the bricks at all.

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
            string[] sS = System.Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);
            List<int> lstA = new List<int>();
            sS = System.Console.ReadLine().Trim().Split(' ');
            for (int i = 0; i < sS.Length; i++)
            {
                lstA.Add(int.Parse(sS[i]) - 1);
            }

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            int iOut = 0;
            Boolean bAllOK = true;                                              // 全部OK？
            for (int i = 0; i < lstA.Count; i++)
            {
                if (lstA[i] != i) { bAllOK = false; break; }                    // 1個でもズレあるか
            }
            if (bAllOK) { iOut = 0; }                                           // 全部OKならここで0で抜ける
            else
            {
                Boolean bExOne = false;                                         // 1個でも1があるか？
                for (int i = 0; i < lstA.Count; i++)
                {
                    if (lstA[i] == 0) { bExOne = true; break; }                 // 1ある
                }
                if (!bExOne) { iOut = -1; }                                     // 1つも1がないと-1で抜ける
                else
                {
                    int iMax = lstA.Count;
                    for (int i = 0; i < iMax; i++)
                    {
                        Boolean bExOK = false;                                  // Noと位置一致？
                        int iNo = -1;
                        for (int j = i; j < lstA.Count; j++)
                        {
                            if (lstA[j] == i) { iNo = j; bExOK = true; break; } // 一致
                        }
                        if (bExOK)
                        {
                            iNo = iNo - i;                                      // 一致したのがあればその前まで破砕
                            for (int j = 1; j <= iNo; j++)
                            {
                                lstA.RemoveAt(i);
                                iOut += 1;
                            }
                        }
                        else
                        {
                            iNo = lstA.Count - i;                               // 一致したのがなければ後ろを全て破砕
                            for (int j = 1; j <= iNo; j++)
                            {
                                lstA.RemoveAt(i);
                                iOut += 1;
                            }
                            break;
                        }
                    }
                }
            }

            // 出力
            System.Console.WriteLine("{0}", iOut.ToString().Trim());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }

}