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/**
 * Find the order of the largest plus sign in a grid with buildings.
 * Dynamic Programming approach.
 *
 * @param {number} n - The size of the grid
 * @param {number[][]} mines - The coordinates of buildings
 * @return {number} - The order of the largest plus sign
 */
function orderOfLargestPlusSign(n, mines) {
  // Initialize grid with all 1's
  const grid = Array(n).fill().map(() => Array(n).fill(1));
 
  // Mark buildings as 0's
  for (const [x, y] of mines) {
    grid[x][y] = 0;
  }
 
  // Initialize arrays to store consecutive 1's in each direction
  const left = Array(n).fill().map(() => Array(n).fill(0));
  const right = Array(n).fill().map(() => Array(n).fill(0));
  const up = Array(n).fill().map(() => Array(n).fill(0));
  const down = Array(n).fill().map(() => Array(n).fill(0));
 
  // Compute left and right arrays
  for (let i = 0; i < n; i++) {
    // Left to right
    for (let j = 0; j < n; j++) {
      if (grid[i][j] === 1) {
        left[i][j] = (j > 0) ? left[i][j - 1] + 1 : 1;
      }
    }
 
    // Right to left
    for (let j = n - 1; j >= 0; j--) {
      if (grid[i][j] === 1) {
        right[i][j] = (j < n - 1) ? right[i][j + 1] + 1 : 1;
      }
    }
  }
 
  // Compute up and down arrays
  for (let j = 0; j < n; j++) {
    // Top to bottom
    for (let i = 0; i < n; i++) {
      if (grid[i][j] === 1) {
        up[i][j] = (i > 0) ? up[i - 1][j] + 1 : 1;
      }
    }
 
    // Bottom to top
    for (let i = n - 1; i >= 0; i--) {
      if (grid[i][j] === 1) {
        down[i][j] = (i < n - 1) ? down[i + 1][j] + 1 : 1;
      }
    }
  }
 
  // Find the largest plus sign
  let maxOrder = 0;
 
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      const order = Math.min(left[i][j], right[i][j], up[i][j], down[i][j]);
      maxOrder = Math.max(maxOrder, order);
    }
  }
 
  return maxOrder;
}
 
/**
 * Find the order of the largest plus sign in a grid with buildings.
 * Optimized Dynamic Programming approach.
 *
 * @param {number} n - The size of the grid
 * @param {number[][]} mines - The coordinates of buildings
 * @return {number} - The order of the largest plus sign
 */
function orderOfLargestPlusSignOptimized(n, mines) {
  // Initialize dp array with maximum possible order
  const dp = Array(n).fill().map(() => Array(n).fill(n));
 
  // Create a set to store building coordinates
  const buildings = new Set();
 
  // Mark buildings
  for (const [x, y] of mines) {
    buildings.add(x * n + y);
    dp[x][y] = 0;
  }
 
  // Process each row and column
  for (let i = 0; i < n; i++) {
    // Left to right
    let count = 0;
    for (let j = 0; j < n; j++) {
      count = buildings.has(i * n + j) ? 0 : count + 1;
      dp[i][j] = Math.min(dp[i][j], count);
    }
 
    // Right to left
    count = 0;
    for (let j = n - 1; j >= 0; j--) {
      count = buildings.has(i * n + j) ? 0 : count + 1;
      dp[i][j] = Math.min(dp[i][j], count);
    }
 
    // Top to bottom
    count = 0;
    for (let j = 0; j < n; j++) {
      count = buildings.has(j * n + i) ? 0 : count + 1;
      dp[j][i] = Math.min(dp[j][i], count);
    }
 
    // Bottom to top
    count = 0;
    for (let j = n - 1; j >= 0; j--) {
      count = buildings.has(j * n + i) ? 0 : count + 1;
      dp[j][i] = Math.min(dp[j][i], count);
    }
  }
 
  // Find the maximum order
  let maxOrder = 0;
 
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      maxOrder = Math.max(maxOrder, dp[i][j]);
    }
  }
 
  return maxOrder;
}
 
/**
 * Find the order of the largest plus sign in a grid with buildings.
 * Brute Force approach.
 *
 * @param {number} n - The size of the grid
 * @param {number[][]} mines - The coordinates of buildings
 * @return {number} - The order of the largest plus sign
 */
function orderOfLargestPlusSignBruteForce(n, mines) {
  // Initialize grid with all 1's
  const grid = Array(n).fill().map(() => Array(n).fill(1));
 
  // Mark buildings as 0's
  for (const [x, y] of mines) {
    grid[x][y] = 0;
  }
 
  // Find the largest plus sign
  let maxOrder = 0;
 
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      if (grid[i][j] === 0) continue;
 
      let order = 0;
 
      // Expand outward from the center
      while (true) {
        const k = order + 1;
 
        // Check if all cells at distance k in all four directions are valid
        if (i - k >= 0 && i + k < n && j - k >= 0 && j + k < n &&
            grid[i - k][j] === 1 && grid[i + k][j] === 1 &&
            grid[i][j - k] === 1 && grid[i][j + k] === 1) {
          order++;
        } else {
          break;
        }
      }
 
      maxOrder = Math.max(maxOrder, order + 1);
    }
  }
 
  return maxOrder;
}
 
// Test cases
console.log(orderOfLargestPlusSign(5, [[4, 2]]));  // 2
console.log(orderOfLargestPlusSign(3, [[0, 0], [0, 2], [2, 0], [2, 2]]));  // 1
console.log(orderOfLargestPlusSign(2, [[0, 0], [0, 1], [1, 0], [1, 1]]));  // 0
 
console.log(orderOfLargestPlusSignOptimized(5, [[4, 2]]));  // 2
console.log(orderOfLargestPlusSignOptimized(3, [[0, 0], [0, 2], [2, 0], [2, 2]]));  // 1
console.log(orderOfLargestPlusSignOptimized(2, [[0, 0], [0, 1], [1, 0], [1, 1]]));  // 0
 
console.log(orderOfLargestPlusSignBruteForce(5, [[4, 2]]));  // 2
console.log(orderOfLargestPlusSignBruteForce(3, [[0, 0], [0, 2], [2, 0], [2, 2]]));  // 1
console.log(orderOfLargestPlusSignBruteForce(2, [[0, 0], [0, 1], [1, 0], [1, 1]]));  // 0