#P1763E. Node Pairs

Node Pairs

Description

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

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

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

The first and only line contains a single integer pp (0p21050 \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 pp-reachable directed graph, and the maximum number of unidirectional pairs of nodes among all such pp-reachable directed graphs with the minimum number of nodes.

Input

The first and only line contains a single integer pp (0p21050 \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 pp-reachable directed graph, and the maximum number of unidirectional pairs of nodes among all such pp-reachable directed graphs with the minimum number of nodes.

样例输入 1

3

样例输出 1

3 0

样例输入 2

4

样例输出 2

5 6

样例输入 3

0

样例输出 3

0 0

Note

In the first test case, the minimum number of nodes required to create a 33-reachable directed graph is 33. Among all 33-reachable directed graphs with 33 nodes, the following graph GG is one of the graphs with the maximum number of unidirectional pairs of nodes, which is 00.