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: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC166.C();
    }
    class ABC166
    {
      public static void A()
      {
        var S = Read.Str();
        Console.WriteLine(S == "ABC" ? "ARC" : "ABC");
      }
      public static void B()
      {
        var N = Read.Int();
        var K = Read.Int();
        var count = new int[N];
        for(int i = 0; i < K; ++i)
        {
          var d = Read.Int();
          var A = Read.IntN();
          foreach(var a in A)
          {
            count[a - 1]++;
          }
        }
        Console.WriteLine(count.Count(x => x == 0));
      }
      public static void C()
      {
        var N = Read.Int();
        var M = Read.Int();
        var H = Read.LongN();
        var Adj = Read.AdjacencyList(N, M);
        var adjMax = new long[N];
        for(int v = 1; v <= N; ++v)
        {
          var h = H[v - 1];
          foreach(var w in Adj[v])
          {
            adjMax[w - 1] = Math.Max(adjMax[w - 1], h);
          }
        }
        Console.WriteLine(Enumerable.Range(0, N).Count(i => H[i] > adjMax[i]));
      }
      public static void D()
      {
        var X = Read.Long();
        var dict = new Dictionary<long, long>();
        for (long i = 0; i <= 1000; ++i)
        {
          dict.Add(i * i * i * i * i, i);
        }
        for (long i = 0; i <= 1000; ++i)
        {
          var A5 = i * i * i * i * i;
          if (dict.ContainsKey(A5 - X))
          {
            Console.WriteLine("{0} {1}", i, dict[A5 - X]);
            return;
          }
          if (dict.ContainsKey((X - A5)))
          {
            Console.WriteLine("{0} {1}", i, -dict[X - A5]);
            return;
          }
        }
      }
      public static void E()
      {
        var N = Read.Int();
        var A = Read.LongN();
        var AP = A.Select((x, i) => x + i + 1).ToArray();
        var AN = A.Select((x, i) => x - i - 1).ToArray();
        var freq = Util.Frequency(AN);
        long sum = 0;
        for(int i = 0; i < N; ++i)
        {
          var v = AP[i];
          sum += freq.ContainsKey(-v) ? freq[-v] - (AN[i] == -v ? 1 : 0) : 0;
        }
        Console.WriteLine(sum);
      }
      public static void F()
      {

      }
    }
    class Util
    {
      public static readonly long P = 1000000007;
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }

      public static int Lowerbound<T1, T2>(SortedList<T1, T2> list, T1 x) where T1 : IComparable<T1>
      {
        return Lowerbound(list.Keys, x);
      }
      public static int Lowerbound<T>(IList<T> list, T x) where T : IComparable<T>
      {
        int min = 0;
        int max = list.Count;
        while (min < max)
        {
          var mid = (min + max) / 2;
          if (list[mid].CompareTo(x) >= 0)
          {
            max = mid;
          }
          else
          {
            min = mid + 1;
          }
        }
        return max;
      }
    }


    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}