#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const int INF = 0x3fffffff;
LL gcd(LL x, LL y) { while(x) swap(x,y%=x); return y; }
static const int dy[] = {-1,+1,0,0};
static const int dx[] = {0,0,-1,+1};
class MeetInTheMaze { public:
int H, W;
map<char, int> count;
void setup_maze(vector<string>& maze)
{
setup_sentinel(maze);
H = maze.size();
W = maze[0].size();
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
count[maze[y][x]] ++;
}
void setup_sentinel(vector<string>& maze)
{
for(int y=0; y<maze.size(); ++y)
maze[y] = '#' + maze[y] + '#';
maze.insert( maze.begin(), string(maze[0].size(), '#') );
maze.insert( maze.end(), string(maze[0].size(), '#') );
}
string ratio2str(LL si, LL bo)
{
if( si >= INF )
return "";
LL g = gcd(si, bo);
stringstream ss;
ss << si/g << "/" << bo/g;
return ss.str();
}
LL dijkstra(const vector< vector<int> >& FD, const vector< vector<int> >& RD, const vector<string>& maze)
{
typedef pair<int,int> vert;
typedef LL cost;
typedef pair<cost,vert> cvert;
vector<bool> V(H*W);
priority_queue< cvert, vector<cvert>, greater<cvert> > Q;
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
if( maze[y][x] != '#' )
Q.push( cvert(FD[y][x]+RD[y][x], make_pair(y,x)) );
cost total = 0;
while( !Q.empty() )
{
cvert v = Q.top(); Q.pop();
cost c = v.first;
int y = v.second.first;
int x = v.second.second;
if( V[y*W+x] )
continue;
V[y*W+x] = true;
if( maze[y][x] == 'L' )
total += c;
for(int k=0; k<4; ++k) {
int yy = y+dy[k];
int xx = x+dx[k];
cvert u(c+1, make_pair(yy,xx));
if( maze[yy][xx]!='#' && !V[yy*W+xx] )
Q.push(u);
}
}
return total;
}
void bfs(vector< vector<int> >& D, vector<string>& m, int y, int x)
{
vector< pair<int,int> > Q(1, make_pair(y,x));
D[y][x] = 0;
for(int s=1; !Q.empty(); ++s)
{
vector< pair<int,int> > Q2;
for(int i=0; i<Q.size(); ++i){
y = Q[i].first;
x = Q[i].second;
for(int k=0; k<4; ++k) {
int yy = y+dy[k];
int xx = x+dx[k];
if( m[yy][xx]!='#' && D[yy][xx]==INF )
Q2.push_back(make_pair(yy,xx)), D[yy][xx]=s;
}
}
Q.swap(Q2);
}
}
string getExpected(vector <string> maze)
{
setup_maze(maze);
LL total = 0;
for(int fy=0; fy<H; ++fy)
for(int fx=0; fx<W; ++fx)
if( maze[fy][fx] == 'F' )
{
// Fill the 2d-map FD with the distance from (fy,fx) in the maze.
vector< vector<int> > FD(H, vector<int>(W, INF));
bfs(FD, maze, fy, fx);
for(int ry=0; ry<H; ++ry)
for(int rx=0; rx<W; ++rx)
if( maze[ry][rx] == 'R' )
{
// Fill the 2d-map RD with the distance from (ry,rx) in the maze.
vector< vector<int> > RD(H, vector<int>(W, INF));
bfs(RD, maze, ry, rx);
// Compute the distances of all the cells from the base "FD+RD"
total += dijkstra(FD, RD, maze);
}
}
return ratio2str(total, count['F']*count['R']*count['L']);
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const string& Expected, const string& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, MeetInTheMaze().getExpected(maze));}
int main(){
CASE(0)
string maze_[] = { "#########",
"####F####",
"##L...R##",
"####L####",
"#########" }
;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = "9/2";
END
CASE(1)
string maze_[] = { "LR",
"RF" }
;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = "2/1";
END
CASE(2)
string maze_[] = { "..F.#...",
"L.F.#..L",
"..F.#...",
".R.#..L.",
"...#....",
"..R#.L.." }
;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = "";
END
CASE(3)
string maze_[] = { ".L..L..L..",
"..........",
"..........",
"..........",
"........R.",
"...R......",
"..........",
"..........",
"..........",
".......F.." }
;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = "40/3";
END
CASE(4)
string maze_[] = { "#.#....#...#.#",
"#...#..#......",
".L#...#R#..#F.",
"#...#......#..",
"#......#.....#",
".R.....F....L.",
"##..#.......#.",
"#........##...",
".F...##L#..#R#" }
;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = "362/27";
END
CASE(5)
string maze_[] = { "LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLFLLLLLLLLLFLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLFFLLLLLLLLLLRLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLRLLLLLFLLLLLLLLLLLLLLF",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLF",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLFLLL",
"LLLLLLLLLLLRLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLRRL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLRLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLR",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLRLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLRLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLRLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLRLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLFFLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"FLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLRLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLRLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLFLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLFLLLLLLLLLRLLLLLLLLLLLLLLLLLLLRLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLFLLLLLLLLLLLLLLLLRLLLLLLLLLRLLLLLLLLLLLLRLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLRLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLFLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLFLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLFLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"FLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLRLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLFLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL",
"LLLLLLLLLLLLLLLLLLLLLLLLLLLFLLLLLLLLLLLLLLLLLLLLLL" }
;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = "210623/4100";
END
/*
CASE(6)
string maze_[] = ;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = ;
END
CASE(7)
string maze_[] = ;
vector <string> maze(maze_, maze_+sizeof(maze_)/sizeof(*maze_));
string _ = ;
END
*/
}
// END CUT HERE