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-csc 3.5.0) (judge verdict: Wrong Answer)

    using System.Collections.Generic;
    using System.Collections;
    using System.IO;
    using System.Linq;
    using System.Text;
    using System;

    namespace cysharp_test
    {
        class Program
        {
            static void Main (string[] args)
            {
                new Program ().solve ();
            }

            void solve ()
            {
                int[] nm = Console.ReadLine ().Split (' ').Select (int.Parse).ToArray ();
                var N = nm[0];
                var M = nm[1];
                var heights = Console.ReadLine ().Split (' ').Select (long.Parse).ToArray ();
                var connections = new List<int>[N];
                for (int i = 0; i < N; i++) connections[i] = new List<int> ();
                for (int i = 0; i < M; i++)
                {
                    var bridges = Console.ReadLine ().Split (' ').Select (int.Parse).ToArray ();
                    connections[bridges[0] - 1].Add (bridges[1] - 1);
                    connections[bridges[1] - 1].Add (bridges[0] - 1);
                }

            bool[] canBe = new bool[N];
            for (int i = 0; i < N;i++)canBe[i] = true;
            int count = 0;
            for (int i = 0; i < N; i++)
                {
                    if(!canBe[i])continue;
                if (connections[i].Count () == 0)
                    {
                        count++;
                    continue;
                    }
                    else
                    {
                        foreach (var n in connections[i])
                        {
                            if ( heights[n] < heights[i])
                            {
                            canBe[n] = false;
                            count++;
                                break;
                            }
                        }

                    }
                }
                Console.WriteLine (count);
                Console.ReadKey ();
            }

        }
        struct Vector2
        {
            public Vector2 (long x, long y)
            {
                this.x = x;
                this.y = y;
            }

            public long x, y;

            public static Vector2 operator + (Vector2 a, Vector2 b)
            {
                return new Vector2 (a.x + b.x, a.y + b.y);
            }

            public static Vector2 operator - (Vector2 a, Vector2 b)
            {
                return new Vector2 (a.x - b.x, a.y - b.y);
            }

            public static Vector2 operator * (Vector2 a, long scala)
            {
                return new Vector2 (a.x * scala, a.y + scala);
            }

            public static bool operator == (Vector2 a, Vector2 b)
            {
                return (a.x == b.x) && (a.y == b.y);
            }

            public static bool operator != (Vector2 a, Vector2 b)
            {
                return !(a.x == b.x) && (a.y == b.y);
            }

            public override int GetHashCode ()
            {
                return (int) (x + y);
            }

            public override bool Equals (object obj)
            {
                if (!(obj == null) && obj is Vector2)
                {
                    return (this == (Vector2) obj);
                }
                else return false;
            }

            public override string ToString ()
            {
                return ("(" + x + "," + y + ")");
            }
        }
    }