A 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. The 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). For 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. Test case 1: No beautiful tree exists with (2) vertices. Hence, print (-1). Test case 2: Test case 3: