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;
using System.Text;
using System.Threading.Tasks;
using System.IO;

namespace ABC
{
    class ABC166F
    {
        const string FILE = "/tmp/data.txt";

        static void Main(string[] args)
        {
#if DEBUG
            Console.SetIn(new StreamReader(FILE));
#endif
            string line;
            string[] sa;
            line = Console.ReadLine();
            sa = line.Split(' ');
            int n = int.Parse(sa[0]);
            int m = int.Parse(sa[1]);

            int[] ha = new int[n];
            line = Console.ReadLine();
            sa = line.Split(' ');

            for (int i = 0; i < n; ++i)
            {
                ha[i] = int.Parse(sa[i]);
            }

            int[,] link = new int[m, 2];
            for (int i = 0; i < m; ++i)
            {
                line = Console.ReadLine();
                sa = line.Split(' ');

                link[i, 0] = int.Parse(sa[0]) - 1;
                link[i, 1] = int.Parse(sa[1]) - 1;
            }

            bool[] res = new bool[n];   // false: 条件にあうもの
            for (int i = 0; i < m; ++i)
            {
                int hl = ha[link[i, 0]];
                int hr = ha[link[i, 1]];

                if (hl == hr)
                {
                    res[link[i, 0]] = true;
                    res[link[i, 1]] = true;
                }
                else if (hl > hr)
                {
                    res[link[i, 1]] = true;
                }
                else
                {
                    res[link[i, 0]] = true;
                }
            }

            int result = 0;
            for (int i = 0; i < n; ++i)
            {
                if (res[i] == false)
                {
                    result += 1;
                }
            }
            Console.WriteLine(result);
#if DEBUG
            Console.WriteLine();
#endif
        }

        private static bool check(int n, int[,] link, int m, int[] ha)
        {
            for (int i = 0; i < m; ++i)
            {
                int h = ha[n];
                if (link[i, 0] == n)
                {
                    int other = ha[link[i, 1]];
                    if (other >= h)
                    {
                        return false;
                    }
                }
                else if (link[i, 1] == n)
                {
                    int other = ha[link[i, 0]];
                    if (other >= h)
                    {
                        return false;
                    }
                }
            }
            return true;
        }
    }
}