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: Runtime Error)

      MODULE stackMod
      IMPLICIT NONE
!Module for STACK : Last in, First out
!reference : プログラミングコンテスト攻略のための
!             アルゴリズムとデータ構造

!2020/05/04 sizeを追加．精度をパラメータに変更．
      integer(16),parameter :: binSize = 10**5
      integer(16),parameter :: precision = 4
      
      type intStack
        private
        !bin(0) must not have any value.
        integer(precision) :: bin(0:binSize) = 0,  top = 0
        
        contains
        procedure,public,pass :: initialize => intInitialize
        procedure,public,pass :: isEmpty    => intIsEmpty
        procedure,public,pass :: isFull     => intIsFull
        procedure,public,pass :: push       => intPush
        procedure,public,pass :: pop        => intPop
        procedure,public,pass :: size       => intSize
      end type
      
      contains
!Reset stack
      subroutine intInitialize( s )
        implicit none
        class(intStack),intent(inout) :: s
        
        s%top = 0
      end subroutine
      
!Check status
      function intIsEmpty( s ) result( TorF )
        implicit none
        class(intStack),intent(in) :: s
        logical :: TorF
        
        if( s%top==0 )then
          TorF = .true.
        else
          TorF = .false.
        endif
      end function
      
      function intIsFull( s ) result( TorF )
        implicit none
        class(intStack),intent(in) :: s
        logical :: TorF
        
        if( s%top>=binSize )then
          TorF = .true.
        else
          TorF = .false.
        endif
      end function
      
!Push into STACK
      subroutine intPush( s,x )
        implicit none
        class(intStack)   ,intent(inout) :: s
        integer(precision),intent(in)    :: x
        
        if( s%isFull() )then
          print*,'Stack is full, Error!';stop
        else
          s%top = s%top + 1
          s%bin(s%top) = x
        endif
      end subroutine
      
!Get from STACK
      function intPop( s ) result( x )
        implicit none
        class(intStack),intent(inout) :: s
        integer(precision) :: x
        
        if( s%isEmpty() )then
          print*,'Stack is empty, Error!';stop
        else
          x = s%bin(s%top)
          s%top = s%top - 1
        end if
      end function
      
!Current STACK size
      function intSize( s ) result( x )
        implicit none
        class(intStack),intent(in) :: s
        integer(precision) :: x
        
        x = s%top
      end function
      
      END MODULE stackMod


      PROGRAM piyo
      use stackMod
      IMPLICIT NONE
      integer,parameter :: prec = 4
      integer(prec) :: n,m
      integer(prec),allocatable :: h(:),a(:),b(:)
      integer(prec) :: i,k,ans
      type(intStack),allocatable :: list(:)
      
      
      read*,n,m
      allocate( h(n), a(m),b(m) )
      read*,h(1:n)
      
      do i = 1,m
        read*,a(i),b(i)
      end do
      
      
      allocate( list(n) )
      
      do i = 1,m
        call list(a(i))%push( b(i) )
        call list(b(i))%push( a(i) )
      end do
      
      
      ans = 0
      outer:do i = 1,n
        
        if( list(i)%size()==0 ) cycle outer
        do k = 1,list(i)%size()
          
          if( list(i)%pop() > h(i) ) cycle outer
          
        end do
        ans = ans + 1
      end do outer
      
      print*,ans
      
      END PROGRAM