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 Sample01
{
    class Program
    {
        static void Main(string[] args)
        {
            var s = Console.ReadLine().Trim().Split(" ").Select(int.Parse).ToArray();
            var hill = Console.ReadLine().Trim().Split(" ").Select(int.Parse).ToArray();
            Hill[] hills = new Hill[s[0]];

            for (int i = 0; i < hill.Length; i++)
            {
                hills[i] = new Hill();
                hills[i].setHigh(hill[i]);
            }

            for (int i = 0; i < s[1]; i++)
            {
                var road = Console.ReadLine().Split(" ").Select(x => int.Parse(x) - 1).ToArray();
                if (hills[road[0]].around < hills[road[0]].High)
                    hills[road[0]].around = hills[road[1]].High;
                if (hills[road[1]].around < hills[road[1]].High)
                    hills[road[1]].around = hills[road[0]].High;
            }

            int count = 0;
            for (int i = 0; i < s[0]; i++)
            {
                if (hills[i].around < hills[i].High)
                    count++;
            }

            Console.WriteLine(count);
        }

        class Hill
        {
            public int around { get; set; } = 0;
            public int High { get; set; }


            public void setHigh(int high)
            {
                High = high;
            }
        }
    }
}