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;
// Thanks to ChatGPT

class main {

static BufferedImage rotateImage(BufferedImage image, double angle) {
  int width = image.getWidth();
  int height = image.getHeight();

  // Calculate new image size to fit rotated image
  double radians = Math.toRadians(angle);
  double sin = Math.abs(Math.sin(radians));
  double cos = Math.abs(Math.cos(radians));
  int newWidth = (int) Math.floor(width * cos + height * sin);
  int newHeight = (int) Math.floor(height * cos + width * sin);

  // Create new image with transparent background
  BufferedImage rotated = new BufferedImage(newWidth, newHeight, BufferedImage.TYPE_INT_ARGB);
  Graphics2D g2d = rotated.createGraphics();
  AffineTransform at = new AffineTransform();

  // Translate to center of image and rotate
  at.translate((newWidth - width) / 2, (newHeight - height) / 2);
  at.rotate(radians, width / 2, height / 2);

  // Draw original image onto new image with transformation
  g2d.setTransform(at);
  g2d.drawImage(image, 0, 0, null);
  g2d.dispose();

  return rotated;
}}