G. Beautiful Treetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA tree is a connected graph without cycles.A tree is called beautiful if the sum of the products of the vertex labels for all its edges is a perfect square.More formally, let $$$E$$$ be the set of edges in the tree. The tree is called beautiful if the value $$$$$$S = \sum_{\{u, v\} \in E} (u \cdot v)$$$$$$ is a perfect square. That is, there exists an integer $$$x$$$ such that $$$S = x^2$$$.You are given an integer $$$n$$$. Your task is to construct a beautiful tree having $$$n$$$ vertices or report that such a tree does not exist.InputThe first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.Each testcase contains a single integer $$$n$$$ ($$$2 \le n \le 2\cdot10^5$$$).It is guaranteed that the sum of $$$n$$$ over all the testcases does not exceed $$$2\cdot10^5$$$.OutputFor each testcase, if there is no beautiful tree having $$$n$$$ vertices, print $$$-1$$$.Otherwise, print $$$n-1$$$ lines denoting the edges of a beautiful tree having $$$n$$$ vertices. Each line should contain two space-separated integers $$$u,v$$$ ($$$1 \le u,v \le n$$$) representing an edge.The vertices can be printed in any order within an edge, and the edges can be printed in any order.ExampleInput3234Output-11 32 31 23 14 1NoteTest case 1: No beautiful tree exists with $$$2$$$ vertices. Hence, print $$$-1$$$.Test case 2: $$$S = (2\cdot3) + (1\cdot3) = 9 = (3)^2$$$ Test case 3: $$$S = (2\cdot1) + (3\cdot1) + (4\cdot1) = 9 = (3)^2$$$