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 Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import qualified Data.ByteString.Char8 as BS
import qualified Data.List as L
import qualified Data.Set as S
import qualified Control.Monad as M
import Data.Maybe (fromJust)
import Data.Ord
import qualified Data.Vector.Unboxed as V

main = do
 [n,k] <- map read <$> words <$> getLine
 h <- V.fromList <$>(1:)<$>map (fst.fromJust.BS.readInt) <$> BS.words<$>BS.getLine
 ab <- L.groupBy (\(x:_) (y:_) -> x == y) <$>L.sortBy (comparing head)<$>concat <$>M.replicateM k gen
 let result = map (tester h) ab
 print ( (length$filter (not .null) result) + (n- (length result))  )

gen = do
 k<-map (fst.fromJust.BS.readInt) <$>BS.words<$>BS.getLine
 return [k,reverse k]

tester hlist list = filter (m>) $map (hlist V.!) checker
 where
  checker = map last list
  m = hlist V.! (head $head list)