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.Collections.Generic;
using System.Linq;

namespace PaizaTest
{
    class Program
    {
        static void Main(string[] args)
        {

            var NM = Console.ReadLine().Split().Select(int.Parse).ToList();

            var H = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var A = new int[NM[1]];
            var B = new int[NM[1]];
            var isGoodObservatories = Enumerable.Repeat(true, NM[0]).ToArray();

            for (int i = 0; i < NM[1]; i++)
            {
                var oneLine = Console.ReadLine().Split().Select(int.Parse).ToArray();
                A[i] = oneLine[0];
                B[i] = oneLine[1];

                // H配列から高さを取得
                var heightA = H[A[i] - 1];
                var heightB = H[B[i] - 1];
                if (heightA > heightB)
                {
                    isGoodObservatories[B[i] - 1] = false;
                }
                else if (heightA < heightB)
                {
                    isGoodObservatories[A[i] - 1] = false;
                } 
                else
                {
                    isGoodObservatories[A[i] - 1] = false;
                    isGoodObservatories[B[i] - 1] = false;
                }
            }

            // いい展望台を下図を求める

            // N個の展望台がある。
            // i番目の展望台の標高はHiである
            // 展望台同士の道はM本あり、jの道はAjとBjをつないでいる


            // 展望台iが良い展望台の条件
            // 1. 展望台iから1本の道を使ってたどり着けるどの展望台よりも標高が高いこと
            // 2. 展望台iから道を使ってたどり着ける展望台がない場合

            // プログラムにすると
            // 1. ある展望台に対して接続された展望台より一番高い
            // 2. ある展望台につながる道が1つもない場合

            Console.WriteLine(isGoodObservatories.Count(x => x));



#if DEBUG
            Console.ReadLine();
#endif
        }
    }
}