平面内有多个矩形，求矩形重叠数最多的区域包含的矩形数量？

import java.util.*;

/**
 * 平面内有多个矩形，求矩形重叠数最多的区域包含的矩形数量？
 * 输入：
 * 3
 * 0 1 1
 * 0 1 1
 * 2 3 4
 * 2 3 4
 * 解释：
 * 3：矩形个数
 * (0,0)矩形1左下端点，(2,2)矩形1右上端点
 * (1,1)矩形2左下端点，(3,3)矩形2右上端点
 * (1,1)矩形3左下端点，(4,4)矩形3右上端点
 * 输出：
 * 3
 *
 */
public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    sc.nextLine();
    HashSet<Integer> rowsSet = new HashSet<>();
    HashSet<Integer> colsSet = new HashSet<>();
    int[][] recs = new int[4][n];
    for (int i = 0; i < 4 * n; i++) {
      int val = sc.nextInt();
      recs[i / n][i % n] = val;
      if ((i / n) % 2 == 0 && !rowsSet.contains(val)) {
        rowsSet.add(val);
      }
      if ((i / n) % 2 == 1 && !colsSet.contains(val)) {
        colsSet.add(val);
      }
    }

    int[] rowsArr = new int[rowsSet.size()];
    int[] colsArr = new int[colsSet.size()];
    Iterator<Integer> rowsIt = rowsSet.iterator();
    int idx = 0;
    while (rowsIt.hasNext()) {
      rowsArr[idx++] = rowsIt.next();
    }
    Arrays.sort(rowsArr);
    Iterator<Integer> colsIt = colsSet.iterator();
    idx = 0;
    while (colsIt.hasNext()) {
      colsArr[idx++] = colsIt.next();
    }
    Arrays.sort(colsArr);
    // 离散化(统计每个小方块的覆盖次数)
    int[][] pieces = new int[rowsSet.size() - 1][colsSet.size() - 1];
    for (int i = 0; i < n; i++) {
      int left = Arrays.binarySearch(rowsArr, recs[0][i]);
      int right = Arrays.binarySearch(rowsArr, recs[2][i]);
      int bottom = Arrays.binarySearch(colsArr, recs[1][i]);
      int top = Arrays.binarySearch(colsArr, recs[3][i]);
      for (int j = left; j < right; j++) {
        for (int k = bottom; k < top; k++) {
          pieces[j][k]++;
        }
      }
    }
    int res = 1;
    for (int i = 0; i < pieces.length; i++) {
      for (int j = 0; j < pieces[0].length; j++) {
        res = Math.max(pieces[i][j], res);
      }
    }
    System.out.println(res);
    sc.close();
  }
}