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.