Note

This problem is an output-only problem (Output Only).

Problem Statement

Output one simple connected undirected graph that satisfies all of the following conditions.

• The number of vertices is $100$, and the vertices are numbered $1,2,\dots ,100$.
• The graph is simple.
  • It has no multiple edges and no self-loops.
• The graph is connected.
• For each $v=1,2,\dots ,100$, the maximum distance from vertex $v$ to any vertex is at least $50$.
  • The distance between vertex $x$ and vertex $y$ is the minimum number of edges contained in a path that starts at vertex $x$ and ends at vertex $y$.

Input

No input is given.

Output

Let $M$ be the number of edges of the graph, and for $i=1,2,\dots ,M$, let the $i$-th edge connect vertices $u_i,v_i$. Output in the following format.

$M$
$u_1$ $v_1$
$u_2$ $v_2$
$\vdots$
$u_M$ $v_M$

Sample

5
1 2
5 1
3 4
99 100
6 28