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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

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

class Program
{
    static void Main(string[] args)
    {
        var input = Console.ReadLine().Split(' ');

        var heightDict = new Dictionary<int, int>();
        var loadDict = new Dictionary<int, HashSet<int>>();

        var towerNum = int.Parse(input[0]);
        var loadNum = int.Parse(input[1]);

        var input2 = Console.ReadLine().Split(' ');
        var i = 1;
        foreach(var n in input2)
        {
            heightDict.Add(i, int.Parse(n));
            i++;
        }

        for (var j = 0; j < loadNum; j++)
        {
            var loads = Console.ReadLine().Split(' ');
            var a = int.Parse(loads[0]);
            var b = int.Parse(loads[1]);
            if (loadDict.ContainsKey(a))
            {
                loadDict[a].Add(b);
            }
            else
            {
                loadDict.Add(a, new HashSet<int>() { b });
            }

            if (loadDict.ContainsKey(b))
            {

                loadDict[b].Add(a);
                
            }
            else
            {
                loadDict.Add(b, new HashSet<int>() { a });
            }
        }

        var ans = 0;
        foreach(var tower in loadDict)
        {
            var flag = true;
            foreach(var otherTower in tower.Value)
            {
                if(heightDict[tower.Key] <= heightDict[otherTower])
                {
                    flag = false;
                }
            }

            if (flag)
            {
                ans += 1;
            }
        }

        for(var j = 1; j < towerNum + 1; j++)
        {
            if (!loadDict.ContainsKey(j))
            {
                ans += 1;
            }
        }

        Console.WriteLine(ans);
        Console.ReadLine();
    }

}