E. Node Pairstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet'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.InputThe first and only line contains a single integer p (0 \le p \le 2 \cdot 10^5) — the number of ordered pairs of nodes.OutputPrint 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.ExamplesInput
3
Output
3 0
Input
4
Output
5 6
Input
0
Output
0 0
NoteIn 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.   
3

3 0 
['dp', 'graphs', 'math', 'number theory', '*2200']