Problem: Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).

He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.

Constraints

* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.

Input

The input is given from Standard Input in the following format:


x_1 y_1
x_2 y_2
x_3 y_3


Output

Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.

Examples

Input

0 0
1 1
2 0


Output

0.292893218813


Input

3 1
1 5
4 9


Output

0.889055514217

Solution (in JAVA):

Solution:

public class Main {

  private static void solve() {
    double[][] p = new double[][] {
      {ni(), ni()},
      {ni(), ni()},
      {ni(), ni()},
    };

    double[] d = new double[3];
    for (int i = 0; i < 3; i ++) {
      int j = (i + 1) % 3;
      int k = (i + 2) % 3;
      double dx = p[j][0] - p[k][0];
      double dy = p[j][1] - p[k][1];
      d[i] = Math.sqrt(dx * dx + dy * dy);
    }
    
    double[] cos = new double[3];
    double[] tan2 = new double[3];
    for (int i = 0; i < 3; i ++) {
      int j = (i + 1) % 3;
      int k = (i + 2) % 3;
      cos[i] = (d[j] * d[j] + d[k] * d[k] - d[i] * d[i]) / (2 * d[j] * d[k]);
      tan2[i] = Math.sqrt((1 - cos[i]) / (1 + cos[i]));
    }

    double ret = 0;
    for (int i = 0; i < 3; i ++) {
      int j = (i + 1) % 3;
      int k = (i + 2) % 3;
      
      double left = 0;
      double right = 1000;
      for (int b = 0; b < 50; b ++) {
        double r = (left + right) / 2;

        double d1 = r / tan2[j];
        double d2 = r / tan2[k];
        
        if (r * 2 <= d[i] - d1 - d2) {
          left = r;
        } else {
          right = r;
        }
      }
      ret = Math.max(ret, left);
    }
    System.out.printf("%.12f\n", ret);
  }
  
  

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = System.getProperty("debug");
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}