Problem: You already know that Valery's favorite sport is biathlon. Due to your help, he learned to shoot without missing, and his skills are unmatched at the shooting range. But now a smaller task is to be performed, he should learn to complete the path fastest.

The track's map is represented by a rectangle n × m in size divided into squares. Each square is marked with a lowercase Latin letter (which means the type of the plot), with the exception of the starting square (it is marked with a capital Latin letters S) and the terminating square (it is marked with a capital Latin letter T). The time of movement from one square to another is equal to 1 minute. The time of movement within the cell can be neglected. We can move from the cell only to side-adjacent ones, but it is forbidden to go beyond the map edges. Also the following restriction is imposed on the path: it is not allowed to visit more than k different types of squares (squares of one type can be visited an infinite number of times). Squares marked with S and T have no type, so they are not counted. But S must be visited exactly once — at the very beginning, and T must be visited exactly once — at the very end.

Your task is to find the path from the square S to the square T that takes minimum time. Among all shortest paths you should choose the lexicographically minimal one. When comparing paths you should lexicographically represent them as a sequence of characters, that is, of plot types.

Input

The first input line contains three integers n, m and k (1 ≤ n, m ≤ 50, n·m ≥ 2, 1 ≤ k ≤ 4). Then n lines contain the map. Each line has the length of exactly m characters and consists of lowercase Latin letters and characters S and T. It is guaranteed that the map contains exactly one character S and exactly one character T.

Pretest 12 is one of the maximal tests for this problem.

Output

If there is a path that satisfies the condition, print it as a sequence of letters — the plot types. Otherwise, print "-1" (without quotes). You shouldn't print the character S in the beginning and T in the end.

Note that this sequence may be empty. This case is present in pretests. You can just print nothing or print one "End of line"-character. Both will be accepted.

Examples

Input

5 3 2
Sba
ccc
aac
ccc
abT


Output

bcccc


Input

3 4 1
Sxyy
yxxx
yyyT


Output

xxxx


Input

1 3 3
TyS


Output

y


Input

1 4 1
SxyT


Output

-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
char field[50][50];
bool used[50][50];
int n, m, k;
int counts[26];
int cur_set;
set<string> min_ways;
int min_len = INT_MAX;
int start_x, start_y, end_x, end_y;
vector<char> alpha(0);
bool comp(pair<int, int> a, pair<int, int> b) {
  if (field[a.first][a.second] == 'T') return true;
  if (field[b.first][b.second] == 'T') return false;
  return field[a.first][a.second] < field[b.first][b.second];
}
vector<pair<int, int>> find_near(int from_y, int from_x,
                                 const set<char> &from_set) {
  vector<pair<int, int>> near(0);
  if (from_y > 0 && !used[from_y - 1][from_x] &&
      from_set.find(field[from_y - 1][from_x]) != from_set.end())
    near.push_back(make_pair(from_y - 1, from_x));
  if (from_y < n - 1 && !used[from_y + 1][from_x] &&
      from_set.find(field[from_y + 1][from_x]) != from_set.end())
    near.push_back(make_pair(from_y + 1, from_x));
  if (from_x > 0 && !used[from_y][from_x - 1] &&
      from_set.find(field[from_y][from_x - 1]) != from_set.end())
    near.push_back(make_pair(from_y, from_x - 1));
  if (from_x < m - 1 && !used[from_y][from_x + 1] &&
      from_set.find(field[from_y][from_x + 1]) != from_set.end())
    near.push_back(make_pair(from_y, from_x + 1));
  sort(near.begin(), near.end(), comp);
  return near;
}
set<char> find_set_near(int from_y, int from_x) {
  set<char> near = set<char>();
  if (from_y > 0 && !used[from_y - 1][from_x])
    near.insert(field[from_y - 1][from_x]);
  if (from_y < n - 1 && !used[from_y + 1][from_x])
    near.insert(field[from_y + 1][from_x]);
  if (from_x > 0 && !used[from_y][from_x - 1])
    near.insert(field[from_y][from_x - 1]);
  if (from_x < m - 1 && !used[from_y][from_x + 1])
    near.insert(field[from_y][from_x + 1]);
  near.erase('T');
  near.erase('S');
  return near;
}
set<char> find_second_near_set(int from_y, int from_x, set<char> &not_from) {
  bool l2, l1, r1, r2, u1, u2, d1, d2;
  l2 = from_x - 2 >= 0;
  l1 = from_x > 0;
  r1 = from_x + 2 < m;
  r2 = from_x + 1 < m;
  u2 = from_y - 2 >= 0;
  u1 = from_y > 0;
  d1 = from_y + 1 < n;
  d2 = from_y + 2 < n;
  int yu2 = from_y - 2;
  int yu1 = from_y - 1;
  int yd1 = from_y + 1;
  int yd2 = from_y + 2;
  int xl2 = from_x - 2;
  int xl1 = from_x - 1;
  int xr1 = from_x + 1;
  int xr2 = from_x + 2;
  set<char> ret = set<char>();
  if (l1 && u2) ret.insert(field[yu2][xl1]);
  if (u2) ret.insert(field[yu2][from_x]);
  if (u2 && r1) ret.insert(field[yu2][xr1]);
  if (r2) {
    if (u1) ret.insert(field[yu1][xr2]);
    ret.insert(field[from_y][xr2]);
    if (d1) ret.insert(field[yd1][xr2]);
  }
  if (d2) {
    if (r1) ret.insert(field[yd2][xr1]);
    ret.insert(field[yd2][from_x]);
    if (l1) ret.insert(field[yd2][xl1]);
  }
  if (l2) {
    if (d1) ret.insert(field[yd1][xl2]);
    ret.insert(field[from_y][xl2]);
    if (u1) ret.insert(field[yu1][xl2]);
  }
  for (set<char>::iterator i = not_from.begin(); i != not_from.end(); i++)
    ret.erase(*i);
  return ret;
}
void read() {
  set<char> set_alpha = set<char>();
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      cin >> field[i][j];
      if (field[i][j] == 'S') {
        start_y = i;
        start_x = j;
      } else if (field[i][j] == 'T') {
        end_y = i;
        end_x = j;
      } else
        set_alpha.insert(field[i][j]);
    }
  for (set<char>::iterator i = set_alpha.begin(); i != set_alpha.end(); i++)
    alpha.push_back(*i);
}
struct cell {
  pair<int, int> pos;
  string s;
};
struct comp2 {
  bool operator()(const cell &a, const cell &b) {
    if (a.s.size() != b.s.size())
      return a.s.size() < b.s.size();
    else
      return a.s < b.s;
  }
};
set<set<char>> last_sets;
bool wave(set<char> &cur_set) {
  if (last_sets.find(cur_set) != last_sets.end())
    return false;
  else
    last_sets.insert(cur_set);
  memset(used, false, 2500);
  used[start_y][start_x] = true;
  cur_set.insert('T');
  multiset<cell, comp2> myque;
  cell tmp;
  tmp.pos = make_pair(start_y, start_x);
  tmp.s = string("");
  myque.insert(tmp);
  while (!myque.empty()) {
    cell cur_cell = *myque.begin();
    myque.erase(myque.begin());
    if (cur_cell.s.length() > min_len) break;
    vector<pair<int, int>> near =
        find_near(cur_cell.pos.first, cur_cell.pos.second, cur_set);
    for (vector<pair<int, int>>::iterator i = near.begin(); i != near.end();
         i++) {
      if (field[i->first][i->second] == 'T') {
        if (cur_cell.s.length() < min_len) {
          min_ways.clear();
          min_len = cur_cell.s.length();
        }
        min_ways.insert(cur_cell.s);
        break;
      }
      used[i->first][i->second] = true;
      cell tmp = cur_cell;
      tmp.pos = *i;
      tmp.s.push_back(field[i->first][i->second]);
      myque.insert(tmp);
    }
  }
  cur_set.erase('T');
  return false;
}
int main() {
  read();
  string s("");
  set<char> start_set = find_set_near(start_y, start_x);
  set<char> end_set = find_set_near(end_y, end_x);
  int l = alpha.size();
  set<char> cur_set = set<char>();
  if (!l)
    wave(cur_set);
  else {
    for (set<char>::iterator a = start_set.begin(); a != start_set.end(); a++) {
      cur_set.insert(*a);
      if (cur_set.size() == k || l < k && cur_set.size() == l)
        wave(cur_set);
      else {
        for (set<char>::iterator b = end_set.begin(); b != end_set.end(); b++) {
          cur_set.insert(*b);
          if (cur_set.size() == k || l < k && cur_set.size() == l)
            wave(cur_set);
          else {
            for (int i = 0; i < l; i++) {
              if (cur_set.end() != cur_set.find(alpha[i])) continue;
              cur_set.insert(alpha[i]);
              if (cur_set.size() == k || l < k && cur_set.size() == l)
                wave(cur_set);
              else {
                for (int j = i + 1; j < l; j++) {
                  if (cur_set.end() != cur_set.find(alpha[j])) continue;
                  cur_set.insert(alpha[j]);
                  if ((*a) == (*b) && cur_set.size() < k) {
                    set<char> second_set =
                        find_second_near_set(start_y, start_x, cur_set);
                    if (!second_set.size())
                      wave(cur_set);
                    else {
                      for (set<char>::iterator p = second_set.begin();
                           p != second_set.end(); p++) {
                        cur_set.insert(*p);
                        wave(cur_set);
                        cur_set.erase(*p);
                      }
                    }
                  } else
                    wave(cur_set);
                  cur_set.erase(alpha[j]);
                }
              }
              cur_set.erase(alpha[i]);
            }
          }
          cur_set.erase(*b);
        }
      }
      cur_set.erase(*a);
    }
  }
label_end:
  if (min_len == INT_MAX)
    cout << "-1";
  else
    cout << (*min_ways.begin());
}