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.IO;

class Program {
  static void Main(string[] args) {
    int ans= 0;
    int[] buf = Array.ConvertAll(Console.ReadLine().Split(' '), aliceTemp => Convert.ToInt32(aliceTemp));
    int N = buf[0];
    int M = buf[1];
    int[] H = Array.ConvertAll(Console.ReadLine().Split(' '), aliceTemp => Convert.ToInt32(aliceTemp));
    int[,]  path = new int[M,2];
    for (int i = 0; i < M; i++)
    {
      int[] temp = Array.ConvertAll(Console.ReadLine().Split(' '), aliceTemp => Convert.ToInt32(aliceTemp));
      path[i,0] = temp[0];    
      path[i,1] = temp[1];  

    }
    for (int w = 0; w < M; w++)
    {
      for (int q = w+1; q < M; q++)
      {
        if (path[w,0] == path[q,0] &&  path[w,1] == path[q,1] )
        {
          path[w,0] = -1;
          path[w,1] = -1;
          continue;
        }
        if (path[w,1] == path[q,0] &&  path[w,0] == path[q,1])
        {
          path[w,0] = -1;
          path[w,1] = -1;
          continue;
        }
      }
    }

    for (int i = 0; i < N; i++)
    { 
      bool con = true;
      for (int j = 0; j < path.GetLength(0); j++)
      {
        if ((path[j,0] -1) == i)
        {
          if (H[path[j,0] -1] < H[path[j,1] -1])
          {
            con = false;
            break;
          }
        }
        if ((path[j,1] -1) == i)
        {
          if (H[path[j,1] -1] < H[path[j,0] -1])
          {
            con = false;
            break;
          }
        }
      }
      if (con){
        ans += 1;
      }
    
    }
    Console.WriteLine(ans.ToString());

      return;
  }
}

// static int[] climbingLeaderboard(int[] scores, int[] alice) {
    //   int[] ans = new int[] { 5, 4, 3, 2, 1 };
    //   return ans;
//int[] alice = Array.ConvertAll(Console.ReadLine().Split(' '), aliceTemp => Convert.ToInt32(aliceTemp));

    // }