import java.util.*;
import java.util.zip.*;
import java.util.List;
import java.util.regex.*;
import java.util.concurrent.*;
import java.util.concurrent.atomic.*;
import java.util.concurrent.locks.*;
import javax.swing.*;
import javax.swing.event.*;
import javax.swing.text.*;
import javax.swing.table.*;
import java.io.*;
import java.net.*;
import java.lang.reflect.*;
import java.lang.ref.*;
import java.lang.management.*;
import java.security.*;
import java.security.spec.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import javax.imageio.*;
import java.math.*;
class main {

static double absDoubleMax(Iterable<Double> l) {
  double max = -Double.MAX_VALUE;
  for (double d : unnullForIteration(l))
    max = Math.max(max, abs(d));
  return max;
}

static double absDoubleMax(double[] l) {
  double max = -Double.MAX_VALUE;
  for (double d : unnullForIteration(l))
    max = Math.max(max, abs(d));
  return max;
}

static double absDoubleMax(double[] l, int from, int to) {
  double max = -Double.MAX_VALUE;
  for (int i = from; i < to; i++)
    max = Math.max(max, abs(l[i]));
  return max;
}
static String unnullForIteration(String s) {
  return s == null ? "" : s;
}

static <A> Collection<A> unnullForIteration(Collection<A> l) {
  return l == null ? immutableEmptyList() : l;
}

static <A> List<A> unnullForIteration(List<A> l) { return l == null ? immutableEmptyList() : l; }
static int[] unnullForIteration(int[] l) { return l == null ? emptyIntArray() : l; }
static char[] unnullForIteration(char[] l) { return l == null ? emptyCharArray() : l; }
static double[] unnullForIteration(double[] l) { return l == null ? emptyDoubleArray() : l; }

static <A, B> Map<A, B> unnullForIteration(Map<A, B> l) {
  return l == null ? immutableEmptyMap() : l;
}

static <A> Iterable<A> unnullForIteration(Iterable<A> i) {
  return i == null ? immutableEmptyList() : i;
}

static <A> A[] unnullForIteration(A[] a) {
  return a == null ? (A[]) emptyObjectArray() : a;
}

static BitSet unnullForIteration(BitSet b) {
  return b == null ? new BitSet() : b;
}



//ifclass Symbol




static long unnullForIteration(Long l) { return l == null ? 0L : l; }


static float abs(float f) { return Math.abs(f); }
static int abs(int i) { return Math.abs(i); }
static double abs(double d) { return Math.abs(d); }




static <A> List<A> immutableEmptyList() {
  return Collections.emptyList();
}


static int[] emptyIntArray_a = new int[0];
static int[] emptyIntArray() { return emptyIntArray_a; }


static char[] emptyCharArray = new char[0];
static char[] emptyCharArray() { return emptyCharArray; }


static double[] emptyDoubleArray = new double[0];
static double[] emptyDoubleArray() { return emptyDoubleArray; }


static <A, B> Map<A, B> immutableEmptyMap() {
  return Collections.emptyMap();
}


static Object[] emptyObjectArray_a = new Object[0];
static Object[] emptyObjectArray() { return emptyObjectArray_a; }



}