There is a square of m rows and n columns on the ground. A robot moves from a grid of coordinates 0,0. Each time, it can only move one grid in four directions: left, right, up and down, but it can't enter a grid whose digit sum of row coordinates and column coordinates is larger than k. For example, when k is 18, the robot can enter the grid (35,37), because 3+5+3+7 = 18. However, it cannot enter the grid (35,38), because 3+5+3+8 = 19. How many grids can the robot reach?

class SolutionMethod1{
	public int movingCount(int threshold,int rows,int cols){//threshold constraints, rows grid rows, cols grid columns,
		boolean[] visted = new boolean[rows*cols];
		for(int i = 0; i < visted.length; i++)
			visted[i] = false;
		
		int count = movingCountCore(threshold,rows,cols,0,0,visted);
		return count;    //Maximum number of travable squares
	}
	
	public int movingCountCore(int threshold,int rows,int cols,int row,int col,boolean[] visted){
		//threshold; rows grid rows; cols grid rows; row number currently processed by row; column number currently processed by col; visted access tag array
		int count = 0;
		if(check(threshold,rows,cols,row,col,visted)){
			visted[row*cols + col] = true;
			
			count = 1 + movingCountCore(threshold,rows,cols,row - 1,col,visted) +
					movingCountCore(threshold,rows,cols,row,col - 1,visted) + 
					movingCountCore(threshold,rows,cols,row + 1,col,visted) +
					movingCountCore(threshold,rows,cols,row,col + 1,visted);
		}
		return count;  //Maximum number of travable squares
	}
	
	boolean check(int threshold,int rows,int cols,int row,int col,boolean[] visted){
		if(row >= 0 && row < rows && col >= 0 && col < cols
				&& (getDigitSum(row) + getDigitSum(col) <= threshold)
				&& !visted[row* cols + col])
			return true;
		return false;
	}
	
	
	public int getDigitSum(int number){  //Number number
		int sum = 0;
		while(number > 0){
			sum += number%10;
			number /= 10;
		}
		return sum;  //The sum of digits of a number
	}
}
public class Solution {
	public static void main(String[] args){
		Scanner scanner = new Scanner(System.in);
		System.out.println("Please enter restrictions k:");
		int k = scanner.nextInt();
		System.out.println("Please enter the number of rows in the grid. m: ");
		int m = scanner.nextInt();
		System.out.println("Please enter the number of columns in the grid. n:");
		int n = scanner.nextInt();
		
		SolutionMethod1 solution1 = new SolutionMethod1();
		
		scanner.close();
		System.out.println("The number of squares that a matrix can reach is:");
		System.out.println(solution1.movingCount(k, m, n));
	}
}