C. Coin Graph
time limit per test
1 second
memory limit per test
256 megabytes
input
stdin
output
stdout

First of all you must know that the name of this problem is irrelevant to what we want!

You are given an integer s. Find a simple connected graph such that the sum of lengths of the shortest paths between all pairs of its vertices is s.

Input

Input contains a signle integer s. (0 ≤ s ≤ 105)

Output

Print "Impossible" (without the quotes) if there is no graph, satisfying the described conditions. Otherwise in the first line print two space-separated integers n and m — the number of vertices and edges in your graph, respectively. Each of following m lines contain two space-separated integers ui, vi(1 ≤ ui, vi ≤ n, ui ≠ vi) — two vertices, connected by an edge in the resulting graph. If there are several answers you can print any of them.

Examples
Input
1
Output
2 1
1 2
Input
2
Output
Impossible
Input
3
Output
3 3
1 2
2 3
3 1
Input
48
Output
7 6
1 2
1 3
2 4
2 5
3 6
3 7
Note

A graph is simple if it has no self-loops or multiple edges between the same vertices. All edges in a simple graph are unweighted and undirected. A graph is connected if there is a path connecting every pair of vertices.