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.*;
import java.math.BigDecimal;
import java.util.*;

public class Main {

  public static void main(String[] args) throws FileNotFoundException {
    FastReader fr = new FastReader();
    int tc = fr.nextInt();
    BigDecimal err = new BigDecimal("0.41421356237309510");
    while (tc-- > 0) {
      int n = fr.nextInt();
      double ans = 1 / ( Math.tan(Math.PI / (2 * n)));
      System.out.println(ans);
    }
  }
}

class FastReader {

  BufferedReader br;
  StringTokenizer st;

  public FastReader() throws FileNotFoundException {
    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 nextLine() {
    String str = "";
    try {
      str = br.readLine();
    } catch (IOException e) {
      e.printStackTrace();
    }
    return str;
  }
}