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: Accepted)

module Main where
import qualified Data.ByteString.Char8         as BS
import qualified Data.ByteString.Lazy.Char8    as BSL
import qualified Data.ByteString.Builder       as BSB
import           Data.Char                      ( isSpace )
import           Data.List                      ( unfoldr )
import           Control.Monad
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM
import           Data.Tuple
import qualified Data.IntMap                   as Map
import qualified Data.Set                      as Set

main :: IO ()
main = do
  [n, m] <- unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  hs     <- VU.unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  abs    <-
    replicateM m $ unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let es = map (\[a, b] -> (a, b)) abs
  let es' =
        Map.fromListWith Set.union
          $  map (\(x, y) -> (x, Set.singleton y))
          $  es
          ++ map swap es
  let trues = map (isHighest hs es') [1 .. n]
  print $ length $ filter id trues

-- lookups x xs = map snd $ filter ((== x) . fst) xs
isHighest :: VU.Vector Int -> Map.IntMap (Set.Set Int) -> Int -> Bool
isHighest hs es i = case es Map.!? i of
  Just rs ->
    let hs' = Set.map (\r -> hs VU.! (r - 1)) rs
    in  Set.findMax hs' < hs VU.! (i - 1)
  Nothing -> True