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 n = int.Parse(input[0]);
        var m = int.Parse(input[1]);

        var heightMap = new Dictionary<int, int>();
        var dict = new Dictionary<int, List<int>>();

        var hinput = Console.ReadLine().Split(' ');
        for (int i = 0; i < n; i++)
        {
            heightMap[i + 1] = int.Parse(hinput[i]);
            dict[i + 1] = new List<int>();
        }

        for (int i = 0; i < m; i++)
        {
            var wayinput = Console.ReadLine().Split(' ');
            dict[int.Parse(wayinput[0])].Add(int.Parse(wayinput[1]));
            dict[int.Parse(wayinput[1])].Add(int.Parse(wayinput[0]));
        }

        var ans = 0;
        for (int i = 0; i < n; i++)
        {
            if (dict[i + 1].Count == 0)
            {
                ans++;
                continue;
            }
            var heightList = new List<int>();
            foreach (var v in dict[i + 1])
            {
                heightList.Add(heightMap[v]);
            }
            if (heightMap[i + 1] > heightList.Max())
            {
                ans++;
            }
        }
        Console.WriteLine(ans);
    }
}