A15489 | Node Pairs

Let's call an ordered pair of nodes $(u, v)$ in a directed graph unidirectional if $u \neq v$ , there exists a path from $u$ to $v$ , and there are no paths from $v$ to $u$ .

A directed graph is called $p$ -reachable if it contains exactly $p$ ordered pairs of nodes $(u, v)$ such that $u < v$ and $u$ and $v$ are reachable from each other. Find the minimum number of nodes required to create a $p$ -reachable directed graph.

Also, among all such $p$ -reachable directed graphs with the minimum number of nodes, let $G$ denote a graph which maximizes the number of unidirectional pairs of nodes. Find this number.

The first and only line contains a single integer $p$ ( $0 \le p \le 2 \cdot 10^5$ ) — the number of ordered pairs of nodes.

Print a single line containing two integers — the minimum number of nodes required to create a $p$ -reachable directed graph, and the maximum number of unidirectional pairs of nodes among all such $p$ -reachable directed graphs with the minimum number of nodes.