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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

   program abc166c
      implicit none
      integer(8)::n,m
      integer(8),allocatable::h(:),a(:),b(:),flag(:)
      integer(8)::i,j,ans

         read *, n,m
         allocate(h(n),a(m),b(m),flag(n))
         read *, h(1:n)

         do i=1,m
            read *, a(i),b(i)
         end do

         flag=1
         do i=1,m
            if ( h(a(i)) < h(b(i)) ) then
               if (flag(b(i))==0 .or. flag(b(i))==1) then
                  flag(b(i))=1
                  flag(a(i))=0
               end if
            else
               if (flag(a(i))==0 .or. flag(a(i))==1) then
                  flag(a(i))=1
                  flag(b(i))=0
               end if
            end if
         end do

         ans=0
         do i=1,n
            if (flag(i)==1) ans=ans+1
         end do

         print *, ans

   end program abc166c