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;

namespace ABC166C
{
    class Program
    {
        static void Main(string[] args)
        {
            var mo = Console.ReadLine().Split(" ");
            ulong n = ulong.Parse(mo[0]);
            ulong m = ulong.Parse(mo[1]);
            ulong[] h = new ulong[n + 1];
            ulong[] z = new ulong[n + 1];
            ulong[] a = new ulong[m + 1];
            ulong[] b = new ulong[m + 1];
            ulong[] d = new ulong[n + 2];
            ulong y = 0;
            var mm = Console.ReadLine().Split(" ");
            for (ulong i = 1; i <= n; i++)
                h[i] = ulong.Parse(mm[i - 1]);
            ulong x = 0;
            for (ulong i = 1; i <= m; i++)
            {
                var aa = Console.ReadLine().Split(" ");
                a[i] = ulong.Parse(aa[0]);
                b[i] = ulong.Parse(aa[1]);
               
            }



            for (ulong i = 1; i <= m; i++)
            {
                if (h[a[i]] < h[b[i]])
                { 
                    z[a[i]] = 1;
                }
                if (h[b[i]] < h[a[i]])
                {
                    z[b[i]] = 1;
                }
                if(h[a[i]]==h[b[i]])
                {
                    z[a[i]] = 1;
                    z[b[i]] = 1;
                }

                //d[a[i]] = 1;
                //d[b[i]] = 1;
            }
            //for (ulong i = 1; i <= n; i++)
            //{
            //    y += d[i];
            //    Console.Write(d[i]);
            //}
            //y = n - y;
            //Console.WriteLine();

            for (ulong i = 1; i <= n; i++)
            {
                Console.Write(z[i]);
                if (z[i] == 1)
                    x += 1;
            }
            //Console.WriteLine();
            //Console.WriteLine(y);
            Console.WriteLine(n-  x );



        }
    }
}