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 {

static int[] posterizerDefinition(IPosterizer posterizer) {
  var cp = cachePosterizer(posterizer);
  return cp == null ? null : cp.cache;
}
static CachedPosterizer cachePosterizer(IPosterizer posterizer) {
  if (posterizer == null) return null;
  if (posterizer instanceof CachedPosterizer) return ((CachedPosterizer) posterizer);
  return new CachedPosterizer(posterizer);
}




interface IPosterizer extends IF1_IntToInt {}
static class CachedPosterizer implements IPosterizer {
  IPosterizer posterizer;
  int[] cache;

  CachedPosterizer(IPosterizer posterizer) {
  this.posterizer = posterizer;
    makeCache();
  }
  
  // 0..255 to 0..255
  public int get(int brightness) {
    return cache[brightness];
  }
  
  void makeCache() {
    cache = new int[256];
    for (int brightness = 0; brightness < 256; brightness++)
      cache[brightness] = posterizer.get(brightness);
  }
}


static interface IF1_IntToInt {
  int get(int i);
}

}