Problem:
Score : 300 points

Problem Statement

There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i.
There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j.

Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road.
Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road.

How many good observatories are there?

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq H_i \leq 10^9

1 \leq A_i,B_i \leq N

A_i \neq B_i

Multiple roads may connect the same pair of observatories.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
H_1 H_2 ... H_N
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Print the number of good observatories.

Sample Input 1

4 3
1 2 3 4
1 3
2 3
2 4

Sample Output 1

2

From Obs. 1, you can reach Obs. 3 using just one road. The elevation of Obs. 1 is not higher than that of Obs. 3, so Obs. 1 is not good.

From Obs. 2, you can reach Obs. 3 and 4 using just one road. The elevation of Obs. 2 is not higher than that of Obs. 3, so Obs. 2 is not good.

From Obs. 3, you can reach Obs. 1 and 2 using just one road. The elevation of Obs. 3 is higher than those of Obs. 1 and 2, so Obs. 3 is good.

From Obs. 4, you can reach Obs. 2 using just one road. The elevation of Obs. 4 is higher than that of Obs. 2, so Obs. 4 is good.

Thus, the good observatories are Obs. 3 and 4, so there are two good observatories.

Sample Input 2

6 5
8 6 9 1 2 1
1 3
4 2
4 3
4 6
4 6

Sample Output 2

3

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            var solver = new Solver();
            solver.Calc();
        }
    }

    public class Solver
    {
        public struct AB
        {
            public int A;
            public int B;
        }
        public void Calc()
        {

            var p = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            var N = p[0];
            var M = p[1];

            var Hs = Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray();

            var hDic = new Dictionary<int, long>();
            foreach (var i in Enumerable.Range(1, N))
            {
                hDic.Add(i, Hs[i - 1]);
            }

            var sorted = hDic.OrderByDescending(x => x.Value);

            var ABs = new List<AB>();

            foreach (var i in Enumerable.Range(0, M))
            {
                var ab = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
                ABs.Add(new AB { A = ab[0], B = ab[1] });
            }

            var ans = 0;
            var cont = new List<int>();
            var roadCount = M;
            foreach (var d in sorted)
            {
                if (!cont.Contains(d.Key))
                {
                    ans++;
                }

                var deleteCount = 0;
                var deleteNumbers = new List<int>();
                for (var r = 0; r < roadCount; r++)
                {
                    if (ABs[r].A == d.Key)
                    {
                        deleteCount++;
                        if (!cont.Contains(ABs[r].B))
                        {
                            cont.Add(ABs[r].B);
                        }

                        if (!deleteNumbers.Contains(ABs[r].B))
                        {
                            deleteNumbers.Add(r);
                        }
                    }
                    else if (ABs[r].B == d.Key)
                    {
                        deleteCount++;
                        if (!cont.Contains(ABs[r].A))
                        {
                            cont.Add(ABs[r].A);
                        }

                        if (!deleteNumbers.Contains(ABs[r].A))
                        {
                            deleteNumbers.Add(r);
                        }
                    }
                }
                roadCount -= deleteCount;

                foreach(var del in deleteNumbers.OrderByDescending(x=>x))
                {
                    ABs.RemoveAt(del);
                }

            }
            Console.WriteLine(ans);
        }


    }

}