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: Accepted)

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

class Program
{
    static void Main(string[] args)
    {
        var inputs = Console.ReadLine()
            .Split(' ')
            .Select(txt => int.Parse(txt))
            .ToList();
        var N = inputs[0]; //展望台の数
        var M = inputs[1]; //道の数
        var heights = Console.ReadLine()
            .Split(' ')
            .Select(txt => int.Parse(txt))
            .ToList();

        var tenboudaiDict = new Dictionary<int, Tenboudai>();
        foreach (var h in heights)
        {
            var id = tenboudaiDict.Count + 1;
            tenboudaiDict.Add(id, new Tenboudai(id, h));
        }

        for (int i = 0; i < M; i++)
        {
            var nums = Console.ReadLine()
                .Split(' ')
                .Select(txt => int.Parse(txt))
                .ToList();

            var t1 = tenboudaiDict[nums[0]];
            var t2 = tenboudaiDict[nums[1]];

            t1.AddRoute(t2);
            t2.AddRoute(t1);
        }

        Console.WriteLine(tenboudaiDict.Values.Count(t => t.Is良い));
    }

    class Tenboudai
    {
        public int Id { get; }
        public int Height { get; }

        public List<Tenboudai> Routes = new List<Tenboudai>();

        public Tenboudai(int id, int height)
        {
            Id = id;
            Height = height;
        }

        public void AddRoute(Tenboudai t)
        {
            Routes.Add(t);
        }

        public bool Is良い => !Routes.Any() || Routes.All(r => r.Height < this.Height);
    }
}