CF1763E.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 $u \lt v$ 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.

我们称有向图中的一对有序节点 $(u, v)$ 是单向的（unidirectional），如果 $u \neq v$，存在一条从 $u$ 到 $v$ 的路径，但不存在从 $v$ 到 $u$ 的路径。

若一个有向图恰好包含 $p$ 个满足 $u \lt v$ 且 $u$ 与 $v$ 相互可达（即存在从 $u$ 到 $v$ 的路径，也存在从 $v$ 到 $u$ 的路径）的有序节点对 $(u, v)$，则称该有向图为 $p$-可达的（$p$-reachable）。求构造一个 $p$-可达有向图所需的最少节点数。

此外，在所有具有最少节点数的 $p$-可达有向图中，设 $G$ 为其中单向节点对数量最多的一个图。求该最大数量。

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.

第一行且唯一一行包含一个整数 $p$（$0 \le p \le 2 \cdot 10^5$）—— 表示节点的有序对数量。

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.

输出一行，包含两个整数——构造一个 $p$-可达有向图所需的最少节点数，以及在所有具有该最少节点数的 $p$-可达有向图中，单向节点对的最大数目。

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 $0$.

在第一个测试用例中，构造一个 $3$-可达有向图所需的最少节点数为 $3$。在所有含 $3$ 个节点的 $3$-可达有向图中，下图 $G$ 是具有最多单向节点对数量（即 $0$）的图之一。