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: Wrong Answer)

using System;
using System.Linq;
using System.Collections;
namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            var foo = Console.ReadLine().Trim().Split(' ');
            var N = int.Parse(foo[0]);
            var M = int.Parse(foo[1]);

            var bar = Console.ReadLine().Trim().Split(' ');
            var H = bar.Select(x=>int.Parse(x)).ToArray();

            var todai = new bool[H.Length];
            for (int i = 0; i < todai.Length; i++)
            {
                todai[i] = true;
            }
            var sumOfWays = new ArrayList();
            while(M>0){
                var ways = (Console.ReadLine().Trim().Split(' ').Select(x=>int.Parse(x))).ToArray();
                var a = ways[0] - 1;
                var b = ways[1] - 1;
                sumOfWays.Add(a);
                sumOfWays.Add(b);
                todai[a] = a > b;
                todai[b] = b > a;
                M--;
            }
            Console.WriteLine(todai.Where(x=>x).Count() + (N - sumOfWays.ToArray().Distinct().Count()));
            Console.ReadLine();
        }
    }
}