Node Pairs
Description
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.
Input
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.
Output
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.
3
4
0
3 0
5 6
0 0
Note
In the first test case, the minimum number of nodes required to create a $3$-reachable directed graph is $3$. Among all $3$-reachable directed graphs with $3$ nodes, the following graph $G$ is one of the graphs with the maximum number of unidirectional pairs of nodes, which is $0$.
