You are given a directed network of flights i.e. $N$ cities and $M$ one-directional flights. Each city has a particular air quality index value associated with it. Now, your task is to determine the maximum threshold value $X$ such that if the flights incident to or from the cities with air quality index values less than $X$ is canceled then there should exist a reachable component of cities in the network of size at least $K$. A subcomponent of a flight network is considered to be a reachable component if all the cities in that component are connected, this implies that all the flights are reachable from each other via direct or connecting flights.
Note: You can assume that the answer always exists.

Input format

• First line: Three integers $N$, $M$, and $K$
• Next line: $N$ space-separated integers where the $i^{th}$ integer denotes the value associated with the city number $i$
• Next $M$ lines: Two space-separated integers $u$ and $v$ that denote that there is a flight available from the city number $u$ to $v$

Output format
Print the maximum threshold value as described in the problem statement.

Constraints
$1 \le K \le N \le 10^5$
$1 \le M \le 10^6$
$1 \le value \; of \; nodes \le 10^9$