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 sun.awt.image.IntegerComponentRaster;

    import java.io.OutputStream;
    import java.io.IOException;
    import java.io.InputStream;
    import java.io.PrintWriter;
    import java.util.InputMismatchException;
    import java.util.*;
    /**
     * Built using CHelper plug-in
     * Actual solution is at the top
     *
     * @author Manan Patel
     */
    public class Main{
        public static void main(String[] args) {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            InputReader in = new InputReader(inputStream);
            PrintWriter w = new PrintWriter(outputStream);
            Solution solver = new Solution();
           int testCount = Integer.parseInt(in.next());
           for (int i = 1; i <= testCount; i++)
                solver.solve(1 , in, w);
            w.close();
        }

        static class Solution {
            public void solve(int tc, InputReader sc, PrintWriter w) {
               int n = sc.nextInt();
               double pie = 3.141592653589793238;
               double ans = Math.tan(pie / (2 * n));
               w.printf("%.9f", 1 / ans);
               w.println();
            }
        }
        static class f{
            public static long power(long x, int y){
                long res = 1;
                while (y > 0)
                {
                    if ((y & 1) == 1)
                        res = (res*x);
                    y = y >> 1;
                    x = x * x;
                }
                return res;
            }
            public static void sort(int[] arr) {
                int n = arr.length, mid, h, s, l, i, j, k;
                int[] res = new int[n];
                for (s = 1; s < n; s <<= 1) {
                    for (l = 0; l < n - 1; l += (s << 1)) {
                        h = Math.min(l + (s << 1) - 1, n - 1);
                        mid = Math.min(l + s - 1, n - 1);
                        i = l;
                        j = mid + 1;
                        k = l;
                        while (i <= mid && j <= h)
                            res[k++] = (arr[i] <= arr[j] ? arr[i++] : arr[j++]);
                        while (i <= mid)
                            res[k++] = arr[i++];
                        while (j <= h)
                            res[k++] = arr[j++];
                        for (k = l; k <= h; k++)
                            arr[k] = res[k];
                    }
                }
            }

        }

        static class InputReader {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private InputReader.SpaceCharFilter filter;

            public InputReader(InputStream stream) {
                this.stream = stream;
            }

            public int read() {
                if (numChars == -1)
                    throw new InputMismatchException();

                if (curChar >= numChars) {
                    curChar = 0;
                    try {
                        numChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }

                    if (numChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }

            public int nextInt() {
                int c = read();

                while (isSpaceChar(c))
                    c = read();

                int sgn = 1;

                if (c == '-') {
                    sgn = -1;
                    c = read();
                }

                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                while (!isSpaceChar(c));

                return res * sgn;
            }

            public long nextLong() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                long res = 0;

                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                while (!isSpaceChar(c));
                return res * sgn;
            }

            public String readString() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = read();
                }
                while (!isSpaceChar(c));

                return res.toString();
            }

            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

            public String next() {
                return readString();
            }

            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);

            }

        }

    }