Mr. Chanek has a new game called Dropping Balls. Initially, Mr. Chanek has a grid a of size n × m

Each cell (x,y) contains an integer a_{x,y} denoting the direction of how the ball will move.

  * a_{x,y}=1 — the ball will move to the right (the next cell is (x, y + 1)); 
  * a_{x,y}=2 — the ball will move to the bottom (the next cell is (x + 1, y)); 
  * a_{x,y}=3 — the ball will move to the left (the next cell is (x, y - 1)). 



Every time a ball leaves a cell (x,y), the integer a_{x,y} will change to 2. Mr. Chanek will drop k balls sequentially, each starting from the first row, and on the c_1, c_2, ..., c_k-th (1 ≤ c_i ≤ m) columns.

Determine in which column each ball will end up in (position of the ball after leaving the grid).

Input

The first line contains three integers n, m, and k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 10^5) — the size of the grid and the number of balls dropped by Mr. Chanek.

The i-th of the next n lines contains m integers a_{i,1},a_{i,2},…,a_{i,m} (1 ≤ a_{i,j} ≤ 3). It will satisfy a_{i, 1} ≠ 3 and a_{i, m} ≠ 1.

The next line contains k integers c_1, c_2, …, c_k (1 ≤ c_i ≤ m) — the balls' column positions dropped by Mr. Chanek sequentially.

Output

Output k integers — the i-th integer denoting the column where the i-th ball will end.

Examples

Input


5 5 3
1 2 3 3 3
2 2 2 2 2
2 2 2 2 2
2 2 2 2 2
2 2 2 2 2
1 2 1


Output


2 2 1 


Input


1 2 2
1 3
1 2


Output


1 2 

Note

In the first example, the first ball will drop as follows. Note that the cell (1, 1) will change direction to the bottom direction.

<image>

The second and third balls will drop as follows. 

<image>

All balls will be dropped from the first row and on the c_1, c_2, ..., c_k-th columns respectively. A ball will stop dropping once it leaves the grid.
import java.io.*;
import java.util.*;

public class MyClass {
    public static void main(String args[]) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String[] splits = reader.readLine().split(" ");
		int n = Integer.parseInt(splits[0]);
		int m = Integer.parseInt(splits[1]);
		int k = Integer.parseInt(splits[2]);
		int i = 0;
		int[][] grid = new int[n][m];
		while (i < n) {
			String[] cols = reader.readLine().split(" ");
			int c = 0;
			for(String col : cols){
				grid[i][c++] = Integer.parseInt(col);
			}
			i++;
		}
		String[] inpStr = reader.readLine().split(" ");
	    int[] input = new int[k];
	    int pos = 0;
	    for(String in : inpStr) {
	        input[pos++] = Integer.parseInt(in);
	    }
		solve(input, grid);
    }
    
    
    private static void solve(int[] input, int[][] grid) {
        
        StringBuilder result = new StringBuilder();
        for(int i = 0 ; i < input.length;i++) {
            int finalPos = traverse(0, input[i]-1, grid);
            result.append(finalPos+1).append(" ");
        }
        
        System.out.println(result.toString().trim());
    }
    
    
    private static int traverse(int r, int c, int[][] grid) {
        
        if(r == grid.length-1) {
            return c;
        }
        
        if(grid[r][c] == 1) {
            grid[r][c] = 2;
            return traverse(r,c+1,grid);
        } else if(grid[r][c] == 3) {
            grid[r][c] = 2;
            return traverse(r,c-1,grid);
        } else {
            return traverse(r+1,c,grid);
        }
        
    }
}