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.
#include <iostream>
#include <stdio.h>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;

int x = -1;
bool match(const char ch, const char p)
{
    if (ch == '_')
        return true;
    if (ch == 'X')
    {
        if (x == -1)
        {
            x = p;
            return true;
        }
        else
        {
            return x == p;
        }
    }
    return ch == p;
}
int myCount(const int x, bool hasX, bool fx, bool f_, int mul)
{
    int count = mul;
    if (fx)
    {
        if (x == -1)
            count *= 9;
        if (x == '0')
            count = 0;
    }
    if (!fx)
    {
        if (x == -1 && hasX)
            count *= 10;
    }
    if (f_)
    {
        count *= 9;
    }
    return count;
}
int main()
{
    int n, ans = 0;
    char s[11];
    gets_s(s, -1);
    string str(s);
    n = str.length();
    if (n == 0)
    {
        ans = 0;
    }
    else if (n == 1)
    {
        ans = match(s[0], '0');
    }
    else if (n == 2)
    {
        char a = str[n - 2], b = str[n - 1];
        x = -1;
        ans += match(a, '2') && match(b, '5');
        x = -1;
        ans += match(a, '5') && match(b, '0');
        x = -1;
        ans += match(a, '7') && match(b, '5');
    }
    else
    {
        char a = str[n - 2], b = str[n - 1];
        x = -1;
        int mul = 1;
        bool hasX = false;
        bool fx = false;
        bool f_ = false;
        for (int i = 1; i < n - 2; i++)
        {
            if (str[i] == 'X')
                hasX = true;
            if (str[i] == '_')
                mul *= 10;
        }
        if (str[0] == '_')
            f_ = true;
        if (str[0] == 'X')
            fx = true;
        x = -1;
        if (match(a, '2') && match(b, '5'))
        {
            ans += myCount(x, hasX, fx, f_, mul);
        }
        x = -1;
        if (match(a, '7') && match(b, '5'))
        {
            ans += myCount(x, hasX, fx, f_, mul);
        }
        x = -1;
        if (match(a, '5') && match(b, '0'))
        {
            ans += myCount(x, hasX, fx, f_, mul);
        }
        x = -1;
        if (match(a, '0') && match(b, '0'))
        {
            ans += myCount(x, hasX, fx, f_, mul);
        }
        if (str[0] == '0')ans = 0;
    }
    printf("%d", ans);
    return 0;
}