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 java.util.function.*;
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 java.awt.geom.*;
import javax.imageio.*;
import java.math.*;
import java.time.Duration;
import java.lang.invoke.VarHandle;
import java.lang.invoke.MethodHandles;
class main {

interface PriceCells {
  boolean isCellLimit(double price);
  
  // next-higher cell limit or NaN if no more cells
  double nextCellLimit(double price);
  
  // next-lower cell limit or NaN if no more cells
  double previousCellLimit(double price);
  
  // go n steps down
  double nCellLimitsDown(double price, int n);
  
  // go n steps up
  double nCellLimitsUp(double price, int n);
  
  // convert to "cell space" (0=first cell limit, 1=next cell limit, -1=previous cell limit etc)
  default double toCellNumber(double price){ return priceToCellNumber(price); }
double priceToCellNumber(double price);
  
  default double fromCellNumber(double cellNumber){ return cellNumberToPrice(cellNumber); }
double cellNumberToPrice(double cellNumber);
}}