Problem: The statement of this problem is the same as the statement of problem C2. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.

You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.

Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.

You can rotate 2n-gon and/or the square.

Input

The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.

Next T lines contain descriptions of test cases — one per line. Each line contains single even integer n (2 ≤ n ≤ 200). Don't forget you need to embed 2n-gon, not an n-gon.

Output

Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.

Example

Input


3
2
4
200


Output


1.000000000
2.414213562
127.321336469

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;


public class Main {

  public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

  static class FastReader {

    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
      br = new BufferedReader(new
          InputStreamReader(System.in));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }

    long nextLong() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String[] nextSArray() {
      String sr[] = null;
      try {
        sr = br.readLine().trim().split(" ");
      } catch (IOException e) {
        e.printStackTrace();
      }
      return sr;
    }

    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }

      return str;
    }
  }


  public static void main(String[] args) throws Exception {
    FastReader sc = new FastReader();
//
    int t1 = sc.nextInt();

    for (int t = 0; t < t1; ++t) {
      int n = sc.nextInt();
      double side=1/(Math.tan(3.1415926535897/(2*n)));
      out.println(side);
    }
    out.close();



  }
}

// out.println(al.toString().replaceAll("[\\[|\\]|,]",""));