Level Generation

Ivan is developing his own computer game. Now he tries to create some levels for his game. But firstly for each level he needs to draw a graph representing the structure of the level.

Ivan decided that there should be exactly n_i vertices in the graph representing level i, and the edges have to be bidirectional. When constructing the graph, Ivan is interested in special edges called bridges. An edge between two vertices u and v is called a bridge if this edge belongs to every path between u and v (and these vertices will belong to different connected components if we delete this edge). For each level Ivan wants to construct a graph where at least half of the edges are bridges. He also wants to maximize the number of edges in each constructed graph.

So the task Ivan gave you is: given q numbers n₁, n₂, ..., n_q, for each i tell the maximum number of edges in a graph with n_i vertices, if at least half of the edges are bridges. Note that the graphs cannot contain multiple edges or self-loops.