CF1763E.Node Pairs

普及/提高-

通过率：0%

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题目描述

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.

输入格式

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.

输出格式

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.

输入输出样例

输入#1
```
3
```
输出#1
```
3 0
```
输入#2
```
4
```
输出#2
```
5 6
```
输入#3
```
0
```
输出#3
```
0 0
```

说明/提示

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 $0$ .

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