#include <bits/stdc++.h>
using namespace std;
int n, m, k;
int mat[1010][1010];
struct dsu {
  vector<int> parent;
  dsu(int n) {
    parent.resize(n);
    for (int i = 0; i < n; i++) parent[i] = i;
  }
  int find_set(int a) {
    if (parent[a] == a) return a;
    return parent[a] = find_set(parent[a]);
  }
  int merge(int a, int b) {
    int x = find_set(a), y = find_set(b);
    parent[x] = y;
    return x;
  }
  bool are_same(int a, int b) { return find_set(a) == find_set(b); }
  int size(int a) { return -parent[find_set(a)]; }
};
inline int coord(int i, int j) { return i * m + j; }
inline pair<int, int> coord(int hash) { return {hash / m, hash % m}; }
int main() {
  cin >> n >> m >> k;
  dsu dsu(1001123);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      scanf("%d", &mat[i][j]);
    }
  }
  for (int i = 0; i < k; i++) {
    int c;
    cin >> c;
    c--;
    int row = 0;
    while (row < n) {
      int current_cell = mat[row][c];
      if (current_cell == 1) {
        mat[row][c] = 2;
        dsu.merge(coord(row, c), coord(row + 1, c));
        c++;
      } else if (current_cell == 3) {
        mat[row][c] = 2;
        dsu.merge(coord(row, c), coord(row + 1, c));
        c--;
      } else {
        int new_step = dsu.find_set(coord(row, c));
        if (!dsu.are_same(coord(row, c), coord(row + 1, c)))
          dsu.merge(coord(row, c), coord(row + 1, c));
        auto next_coord = coord(new_step);
        row = next_coord.first;
        c = next_coord.second;
        continue;
      }
    }
    printf("%d ", c + 1);
  }
  cout << endl;
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n, m, k;
int mat[1010][1010];
struct dsu {
  vector<int> parent;
  dsu(int n) {
    parent.resize(n);
    for (int i = 0; i < n; i++) parent[i] = i;
  }
  int find_set(int a) {
    if (parent[a] == a) return a;
    return parent[a] = find_set(parent[a]);
  }
  int merge(int a, int b) {
    int x = find_set(a), y = find_set(b);
    parent[x] = y;
    return x;
  }
  bool are_same(int a, int b) { return find_set(a) == find_set(b); }
  int size(int a) { return -parent[find_set(a)]; }
};
inline int coord(int i, int j) { return i * m + j; }
inline pair<int, int> coord(int hash) { return {hash / m, hash % m}; }
int main() {
  cin >> n >> m >> k;
  dsu dsu(1001123);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      scanf("%d", &mat[i][j]);
    }
  }
  for (int i = 0; i < k; i++) {
    int c;
    cin >> c;
    c--;
    int row = 0;
    while (row < n) {
      int current_cell = mat[row][c];
      if (current_cell == 1) {
        mat[row][c] = 2;
        dsu.merge(coord(row, c), coord(row + 1, c));
        c++;
      } else if (current_cell == 3) {
        mat[row][c] = 2;
        dsu.merge(coord(row, c), coord(row + 1, c));
        c--;
      } else {
        int new_step = dsu.find_set(coord(row, c));
        if (!dsu.are_same(coord(row, c), coord(row + 1, c)))
          dsu.merge(coord(row, c), coord(row + 1, c));
        auto next_coord = coord(new_step);
        row = next_coord.first;
        c = next_coord.second;
        continue;
      }
    }
    printf("%d ", c + 1);
  }
  cout << endl;
  return 0;
}

```