Google Code Jam 2012 Qualification Round

Brief description:

Problem D. Hall of Mirrors
給定一個鏡中世界.. . 問點光源處有多少束光線可以在 D 射程內反射回來。
( D <= 50,鏡子只有水平和豎直兩種.. .)

Analysis:

比賽的時候寫的是發射扇形的區間。。。並在反射過程中不斷細分細分。。。
(仍然有待實現。。)

看了代碼發現很多人利用運動的相對性。。將平面沿著鏡面的反射方向進行平鋪。。。
這樣處理後可以保證光束自始自終是一條直線。。。。其實上述思路的真正意義是對解進行離散化。。。

(裸計算幾何方法比較無腦。。小數據大概都要跑 7 分鐘吧。。還有一些噁心的精度問題。。)
(。。。)

/** ` Micro Mezzo Macro Flation -- Overheated Economy ., **/

#include <algorithm>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <cstring>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>

using namespace std;

#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_C(i, n) for (int n____=int(n),i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=int(b),i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=int(a),i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_C(i, n) for (int n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=int(a),i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
#define REP_C_N(i, n) for (n____=int(n),i=0;i<n____;++i)
#define FOR_C_N(i, a, b) for (b____=int(b),i=a;i<b____;++i)
#define DWN_C_N(i, b, a) for (a____=int(a),i=b-1;i>=a____;--i)
#define REP_1_C_N(i, n) for (n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (a____=int(a),i=b;i>=a____;--i)

#define ECH(it, A) for (typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define DO(n) while(n--)
#define DO_C(n) int n____ = n; while(n____--)
#define TO(i, a, b) int s_=a<b?1:-1,b_=b+s_;for(int i=a;i!=b_;i+=s_)
#define TO_1(i, a, b) int s_=a<b?1:-1,b_=b;for(int i=a;i!=b_;i+=s_)
#define SQZ(i, j, a, b) for (int i=int(a),j=int(b)-1;i<j;++i,--j)
#define SQZ_1(i, j, a, b) for (int i=int(a),j=int(b);i<=j;++i,--j)
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)

#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define BSC(A, X) find(ALL(A), X) // != A.end()
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int(A.size())
#define PB push_back
#define MP(A, B) make_pair(A, B)

#define Rush int T____; RD(T____); DO(T____)
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define Ruby system("ruby main.rb")
#define Haskell system("runghc main.hs")
#define Pascal system("fpc main.pas")

typedef long long LL;
typedef double DB;
typedef unsigned UINT;
typedef unsigned long long ULL;

typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VD;
typedef set<int> SI;
typedef set<string> SS;
typedef set<LL> SL;
typedef set<DB> SD;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef map<LL, int> MLI;
typedef map<DB, int> MDI;
typedef map<int, bool> MIB;
typedef map<string, bool> MSB;
typedef map<LL, bool> MLB;
typedef map<DB, bool> MDB;
typedef pair<int, int> PII;
typedef pair<int, bool> PIB;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
typedef set<PII> SII;
typedef map<PII, int> MPIII;
typedef map<PII, bool> MPIIB;

/** I/O Accelerator **/

/* ... :" We are I/O Accelerator ... Use us at your own risk ;) ... " .. */

template<class T> inline void RD(T &);
template<class T> inline void OT(const T &);

inline int RD(){ int x; RD(x); return x;}
template<class T> inline T& _RD(T &x){ RD(x); return x;}
inline void RC(char &c){scanf(" %c", &c);}
inline void RS(char *s){scanf("%s", s);}

template<class T0, class T1> inline void RD(T0 &x0, T1 &x1){RD(x0), RD(x1);}
template<class T0, class T1, class T2> inline void RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2);}
template<class T0, class T1, class T2, class T3> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);}
template<class T0, class T1> inline void OT(T0 &x0, T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(T0 &x0, T1 &x1, T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}

template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}

template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2){FLC(A0), FLC(A1), FLC(A2);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3){FLC(A0), FLC(A1), FLC(A2), FLC(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5), FLC(A6);}

template<class T> inline void SRT(T &A){sort(ALL(A));}
template<class T, class C> inline void SRT(T &A, C B){sort(ALL(A), B);}

/** Add - On **/

const int MOD = 1000000007;
const int INF = 10009;
const DB EPS = 1e-9;
const DB OO = 1e15;
const DB PI = 3.14159265358979323846264;//M_PI;

// <<= ` 0. Daily Use .,

template<class T> inline void checkMin(T &a,const T b){if (b<a) a=b;}
template<class T> inline void checkMax(T &a,const T b){if (b>a) a=b;}
template <class T, class C> inline void checkMin(T& a, const T b, C c){if (c(b,a)) a = b;}
template <class T, class C> inline void checkMax(T& a, const T b, C c){if (c(a,b)) a = b;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
int Ceil(int x, int y){return (x - 1) / y + 1;}

// <<= ` 1. Bitwise Operation .,

inline bool _1(int x, int i){return x & 1<<i;}
inline int _1(int i){return 1<<i;}
inline int _U(int i){return _1(i) - 1;};

inline int count_bits(int x){
    x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
    x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
    x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
    x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
    x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
    return x;
}

template<class T> inline T low_bit(T x) {
    return x & -x;
}

template<class T> inline T high_bit(T x) {
    T p = low_bit(x);
    while (p != x) x -= p, p = low_bit(x);
    return p;
}

// <<= ` 2. Modular Arithmetic Basic .,

inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a  += MOD; return a;}
inline void MUL(int &a, int b){a = int((LL)a * b % MOD);}
inline int pdt(int a, int b){return int((LL)a * b % MOD);}

// <<= '9. Comutational Geometry .,

struct Po; struct Line; struct Seg;

inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}

struct Po{
    DB x, y;
    Po(DB _x = 0, DB _y = 0):x(_x), y(_y){}

    friend istream& operator >>(istream& in, Po &p){return in >> p.x >> p.y;}
    friend ostream& operator <<(ostream& out, Po p){return out << "(" << p.x << ", " << p.y << ")";}

    friend bool operator ==(Po, Po);
    friend bool operator !=(Po, Po);
    friend Po operator +(Po, Po);
    friend Po operator -(Po, Po);
    friend Po operator *(Po, DB);
    friend Po operator /(Po, DB);

    bool operator < (const Po &rhs) const{return sgn(x, rhs.x) < 0 || sgn(x, rhs.x) == 0 && sgn(y, rhs.y) < 0;}
    Po& operator +=(Po rhs){x += rhs.x, y += rhs.y;}
    Po& operator -=(Po rhs){x -= rhs.x, y -= rhs.y;}
    Po& operator *=(DB k){x *= k, y *= k;}
    Po& operator /=(DB k){x /= k, y /= k;}

    DB length_sqr(){return sqr(x) + sqr(y);}
    DB length(){return sqrt(length_sqr());}

    DB atan(){
        return atan2(y, x);
    }

    void input(){
        int _x, _y; scanf("%d %d", &_x, &_y);
        x = _x, y = _y;
    }
};

bool operator ==(Po a, Po b){return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;}
bool operator !=(Po a, Po b){return sgn(a.x - b.x) != 0 || sgn(a.y - b.y) != 0;}
Po operator +(Po a, Po b){return Po(a.x + b.x, a.y + b.y);}
Po operator -(Po a, Po b){return Po(a.x - b.x, a.y - b.y);}
Po operator *(Po a, DB k){return Po(a.x * k, a.y * k);}
Po operator /(Po a, DB k){return Po(a.x / k, a.y / k);}

struct Line{
    Po a, b;
    Line(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
    Line(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
    Line(Seg);

    friend ostream& operator <<(ostream& out, Line p){return out << p.a << "-" << p.b;}
};

struct Seg{
    Po a, b;
    Seg(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
    Seg(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
    Seg(Line l);

    friend ostream& operator <<(ostream& out, Seg p){return out << p.a << "-" << p.b;}
    DB length(){return (b - a).length();}
};

Line::Line(Seg l):a(l.a), b(l.b){}
Seg::Seg(Line l):a(l.a), b(l.b){}

#define innerProduct dot
#define scalarProduct dot
#define dotProduct dot
#define outerProduct det
#define crossProduct det

inline DB dot(DB x1, DB y1, DB x2, DB y2){return x1 * x2 + y1 * y2;}
inline DB dot(Po a, Po b){return dot(a.x, b.y, b.x, b.y);}
inline DB dot(Po p0, Po p1, Po p2){return dot(p1 - p0, p2 - p0);}
inline DB dot(Line l1, Line l2){return dot(l1.b - l1.a, l2.b - l2.a);}
inline DB det(DB x1, DB y1, DB x2, DB y2){return x1 * y2 - x2 * y1;}
inline DB det(Po a, Po b){return det(a.x, a.y, b.x, b.y);}
inline DB det(Po p0, Po p1, Po p2){return det(p1 - p0, p2 - p0);}
inline DB det(Line l1, Line l2){return det(l1.b - l1.a, l2.b - l2.a);}

template<class T1, class T2> inline DB dist(T1 x, T2 y){return sqrt(dist_sqr(x, y));}

inline DB dist_sqr(Po a, Po b){return sqr(a.x - b.x) + sqr(a.y - b.y);}
inline DB dist_sqr(Po p, Line l){Po v0 = l.b - l.a, v1 = p - l.a; return sqr(fabs(det(v0, v1))) / v0.length_sqr();}
inline DB dist_sqr(Po p, Seg l){
    Po v0 = l.b - l.a, v1 = p - l.a, v2 = p - l.b;
    if (sgn(dot(v0, v1)) * sgn(dot(v0, v2)) <= 0) return dist_sqr(p, Line(l));
    else return min(v1.length_sqr(), v2.length_sqr());
}

inline DB dist_sqr(Line l, Po p){
    return dist_sqr(p, l);
}

inline DB dist_sqr(Line l1, Line l2){
    if (sgn(det(l1, l2)) != 0) return 0;
    return dist_sqr(l1.a, l2);
}
inline DB dist_sqr(Line l1, Seg l2){
    Po v0 = l1.b - l1.a, v1 = l2.a - l1.a, v2 = l2.b - l1.a; DB c1 = det(v0, v1), c2 = det(v0, v2);
    return sgn(c1) != sgn(c2) ? 0 : sqr(min(fabs(c1), fabs(c2))) / v0.length_sqr();
}

inline DB dist_sqr(Seg l, Po p){
    return dist_sqr(p, l);
}

inline DB dist_sqr(Seg l1, Line l2){
    return dist_sqr(l2, l1);
}

bool isIntersect(Seg l1, Seg l2){

    //if (l1.a == l2.a || l1.a == l2.b || l1.b == l2.a || l1.b == l2.b) return true;

    return
        min(l1.a.x, l1.b.x) <= max(l2.a.x, l2.b.x) &&
        min(l2.a.x, l2.b.x) <= max(l1.a.x, l1.b.x) &&
        min(l1.a.y, l1.b.y) <= max(l2.a.y, l2.b.y) &&
        min(l2.a.y, l2.b.y) <= max(l1.a.y, l1.b.y) &&
    sgn( det(l1.a, l2.a, l2.b) ) * sgn( det(l1.b, l2.a, l2.b) ) <= 0 &&
    sgn( det(l2.a, l1.a, l1.b) ) * sgn( det(l2.b, l1.a, l1.b) ) <= 0;

}

inline DB dist_sqr(Seg l1, Seg l2){
    if (isIntersect(l1, l2)) return 0;
    else return min(dist_sqr(l1.a, l2), dist_sqr(l1.b, l2), dist_sqr(l2.a, l1), dist_sqr(l2.b, l1));
}

inline bool isOnExtremePoint(const Po &p, const Seg &l){
    return p == l.a || p == l.b;
}

inline bool isOnseg(const Po &p, const Seg &l){

    //if (p == l.a || p == l.b) return false;

    return sgn(det(p, l.a, l.b)) == 0 &&
        sgn(l.a.x, p.x) * sgn(l.b.x, p.x) <= 0 && sgn(l.a.y, p.y) * sgn(l.b.y, p.y) <= 0;
}



inline Po intersect(const Line &l1, const Line &l2){
    return l1.a + (l1.b - l1.a) * (det(l2.a, l1.a, l2.b) / det(l2, l1));
}

// perpendicular foot
inline Po intersect(const Po & p, const Line &l){
    return intersect(Line(p, p + Po(l.a.y - l.b.y, l.b.x - l.a.x)), l);
}

inline Po rotate(Po p, DB alpha, Po o = Po()){
    p.x -= o.x, p.y -= o .y;
    return Po(p.x * cos(alpha) - p.y * sin(alpha), p.y * cos(alpha) + p.x * sin(alpha)) + o;
}

// <<= ' 0. I/O Accelerator interface .,

template<class T> inline void RD(T &x){
    //cin >> x;
    scanf("%d", &x);
    //char c; for (c = getchar(); c < '0'; c = getchar()); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
    //char c; c = getchar(); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
}

int ____Case;
template<class T> inline void OT(const T &x){
    printf("Case #%d: ", ++____Case);
    printf("%d", x);
    puts("");
}

/* .................................................................................................................................. */

const int N = 39;
char Map[N][N], tmp[N][N];
int n, m, D, X0, Y0, res;

vector<Line> mirror;

struct ray{
    Po p; int dx, dy;
    ray(){}
    ray(Po _p, int _dx, int _dy):p(_p), dx(_dx), dy(_dy){}
    Po p_(){
        return Po(p.x + 2e2*dx, p.y + 2e2*dy);
    }
} cur;

vector<pair<Po, bool> > L; vector<DB> P;
DB _d, d; Po O;


inline Po lb(int x, int y){
    return Po(x * 2 + 2, y * 2);
}

inline Po rb(int x, int y){
    return Po(x * 2 + 2, y * 2 + 2);
}

inline Po lu(int x, int y){
    return Po(x * 2, y * 2);
}

inline Po ru(int x, int y){
    return Po(x * 2, y * 2 + 2);
}

inline Po mm(int x, int y){
    return Po(x * 2 + 1, y * 2 + 1);
}

void init(){

    RST(Map); CLR(mirror); RD(n, m, D); d = D * 2; REP_2(i, j, n, m){
        RC(Map[i][j]); if (Map[i][j] == 'X') X0 = i, Y0 = j, Map[i][j] = '.';
    }

    int _i, _j; CPY(tmp, Map); REP_2(i, j, n, m) if (tmp[i][j] == '#'){
        _j = j, tmp[i][j] = '.';
        while (tmp[i][j+1] == '#'){
            tmp[i][++j] = '.';
        }
        mirror.PB(Line(lb(i, _j), rb(i, j)));
        mirror.PB(Line(lu(i, _j), ru(i, j)));
    }

    CPY(tmp, Map); REP_2(j, i, m, n) if (tmp[i][j] == '#'){
        _i = i, tmp[i][j] = '.';
        while (tmp[i+1][j] == '#'){
            tmp[++i][j] = '.';
        }
        mirror.PB(Line(lu(_i, j), lb(i, j)));
        mirror.PB(Line(ru(_i, j), rb(i, j)));
    }


/*
    REP(i, SZ(mirror)){
        cout << mirror[i] << endl;
    }

    cout << "----" << endl;
*/

    O = mm(X0, Y0), res = 0;
}

bool comp(pair<Po, bool> a, pair<Po, bool> b){
    return dist_sqr(cur.p, a.first) <= dist_sqr(cur.p, b.first);
}

int main(){

    freopen("D-large-practice.in", "r", stdin);
    //freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);

    Rush{

        init(); FOR_1(i, -D, D) FOR_1(j, -D, D){

            if (!i && abs(j) != 1) continue;
            if (!j && abs(i) != 1) continue;
            if (i && j && abs(__gcd(i, j)) != 1) continue;
            if (sqr(i)+sqr(j) > sqr(D)) continue;

            cur = ray(O, i, j), _d = 0;

            while (true){

                Line l = Line(cur.p, cur.p_());

                CLR(L, P); REP(ii, SZ(mirror)) if (!isOnseg(cur.p, mirror[ii])){
                    Po p = intersect(l, mirror[ii]);
                    if (isOnseg(p, l)){
                        if (isOnExtremePoint(p, mirror[ii])) P.PB(dist_sqr(cur.p, p));
                        else if (isOnseg(p, mirror[ii])) L.PB(MP(p, !sgn(mirror[ii].a.x, mirror[ii].b.x)));
                    }
                }

                sort(ALL(L), comp), SRT(P);

                if (!P.empty() && sgn(P[0], dist_sqr(cur.p, L[0].first)) < 0){

                    bool bx = false, by = false; REP(ii, SZ(mirror)) if (!isOnseg(cur.p, mirror[ii])){
                        Po p = intersect(l, mirror[ii]);
                        if (isOnseg(p, l)){
                            if (isOnExtremePoint(p, mirror[ii])){
                                if (!sgn(dist_sqr(cur.p, p), P[0])){
                                    if (!sgn(mirror[ii].a.x, mirror[ii].b.x)){
                                        if ( (min(mirror[ii].a.y, mirror[ii].b.y) == p.y) ^ (j<0) ) by = true;
                                    }
                                    else {
                                        if ( (min(mirror[ii].a.x, mirror[ii].b.x) == p.x) ^ (i<0) ) bx = true;
                                    }
                                }
                            }
                        }

                        if (bx && by) break;
                    }

                    if (bx && by) break;
                }


                if (cur.p != O && isOnseg(O, l) && dist_sqr(cur.p, O) < dist_sqr(cur.p, L[0].first)){
                    if ( sgn(_d + dist(cur.p, O), d) <= 0) ++res;
                    break;
                }

                _d += dist(cur.p, L[0].first); if (sgn(_d, d) >= 0) break;

                cur.p = L[0].first; if (SZ(L) >= 2 && !sgn(dist(cur.p, L[0].first) , dist(cur.p, L[1].first))){
                    cur.dx = -cur.dx, cur.dy = -cur.dy;
                }
                else {
                    if (L[0].second) cur.dx = -cur.dx;
                    else cur.dy = -cur.dy;
                }
            }
        }

        OT(res);
        cerr << "Case: " << ____Case << endl;
    }
}
/** ` Micro Mezzo Macro Flation -- Overheated Economy ., **/

#include <algorithm>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <cstring>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>

using namespace std;

#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_C(i, n) for (int n____=int(n),i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=int(b),i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=int(a),i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_C(i, n) for (int n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=int(a),i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
#define REP_C_N(i, n) for (n____=int(n),i=0;i<n____;++i)
#define FOR_C_N(i, a, b) for (b____=int(b),i=a;i<b____;++i)
#define DWN_C_N(i, b, a) for (a____=int(a),i=b-1;i>=a____;--i)
#define REP_1_C_N(i, n) for (n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (a____=int(a),i=b;i>=a____;--i)

#define ECH(it, A) for (typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define DO(n) while(n--)
#define DO_C(n) int n____ = n; while(n____--)
#define TO(i, a, b) int s_=a<b?1:-1,b_=b+s_;for(int i=a;i!=b_;i+=s_)
#define TO_1(i, a, b) int s_=a<b?1:-1,b_=b;for(int i=a;i!=b_;i+=s_)
#define SQZ(i, j, a, b) for (int i=int(a),j=int(b)-1;i<j;++i,--j)
#define SQZ_1(i, j, a, b) for (int i=int(a),j=int(b);i<=j;++i,--j)
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)

#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define BSC(A, X) find(ALL(A), X) // != A.end()
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int(A.size())
#define PB push_back
#define MP(A, B) make_pair(A, B)

#define Rush int T____; RD(T____); DO(T____)
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define Ruby system("ruby main.rb")
#define Haskell system("runghc main.hs")
#define Pascal system("fpc main.pas")

typedef long long LL;
typedef double DB;
typedef unsigned UINT;
typedef unsigned long long ULL;

typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VD;
typedef set<int> SI;
typedef set<string> SS;
typedef set<LL> SL;
typedef set<DB> SD;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef map<LL, int> MLI;
typedef map<DB, int> MDI;
typedef map<int, bool> MIB;
typedef map<string, bool> MSB;
typedef map<LL, bool> MLB;
typedef map<DB, bool> MDB;
typedef pair<int, int> PII;
typedef pair<int, bool> PIB;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
typedef set<PII> SII;
typedef map<PII, int> MPIII;
typedef map<PII, bool> MPIIB;

/** I/O Accelerator **/

/* ... :" We are I/O Accelerator ... Use us at your own risk ;) ... " .. */

template<class T> inline void RD(T &);
template<class T> inline void OT(const T &);

inline int RD(){ int x; RD(x); return x;}
template<class T> inline T& _RD(T &x){ RD(x); return x;}
inline void RC(char &c){scanf(" %c", &c);}
inline void RS(char *s){scanf("%s", s);}

template<class T0, class T1> inline void RD(T0 &x0, T1 &x1){RD(x0), RD(x1);}
template<class T0, class T1, class T2> inline void RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2);}
template<class T0, class T1, class T2, class T3> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);}
template<class T0, class T1> inline void OT(T0 &x0, T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(T0 &x0, T1 &x1, T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}

template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}

template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2){FLC(A0), FLC(A1), FLC(A2);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3){FLC(A0), FLC(A1), FLC(A2), FLC(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5), FLC(A6);}

template<class T> inline void SRT(T &A){sort(ALL(A));}
template<class T, class C> inline void SRT(T &A, C B){sort(ALL(A), B);}

/** Add - On **/

const int MOD = 1000000007;
const int INF = 0x7fffffff;
const DB EPS = 1e-9;
const DB OO = 1e15;
const DB PI = 3.14159265358979323846264;//M_PI;

// <<= ` 0. Daily Use .,

template<class T> inline void checkMin(T &a,const T b){if (b<a) a=b;}
template<class T> inline void checkMax(T &a,const T b){if (b>a) a=b;}
template <class T, class C> inline void checkMin(T& a, const T b, C c){if (c(b,a)) a = b;}
template <class T, class C> inline void checkMax(T& a, const T b, C c){if (c(a,b)) a = b;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
int Ceil(int x, int y){return (x - 1) / y + 1;}

// <<= ` 1. Bitwise Operation .,

inline bool _1(int x, int i){return x & 1<<i;}
inline int _1(int i){return 1<<i;}
inline int _U(int i){return _1(i) - 1;};

inline int count_bits(int x){
    x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
    x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
    x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
    x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
    x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
    return x;
}

template<class T> inline T low_bit(T x) {
    return x & -x;
}

template<class T> inline T high_bit(T x) {
    T p = low_bit(x);
    while (p != x) x -= p, p = low_bit(x);
    return p;
}

// <<= '9. Comutational Geometry .,

struct Po; struct Line; struct Seg;

inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}

struct Po{
    DB x, y;
    Po(DB _x = 0, DB _y = 0):x(_x), y(_y){}

    friend istream& operator >>(istream& in, Po &p){return in >> p.x >> p.y;}
    friend ostream& operator <<(ostream& out, Po p){return out << "(" << p.x << ", " << p.y << ")";}

    friend bool operator ==(Po, Po);
    friend Po operator +(Po, Po);
    friend Po operator -(Po, Po);
    friend Po operator *(Po, DB);
    friend Po operator /(Po, DB);

    bool operator < (const Po &rhs) const{return sgn(x, rhs.x) < 0 || sgn(x, rhs.x) == 0 && sgn(y, rhs.y) < 0;}
    Po& operator +=(Po rhs){x += rhs.x, y += rhs.y;}
    Po& operator -=(Po rhs){x -= rhs.x, y -= rhs.y;}
    Po& operator *=(DB k){x *= k, y *= k;}
    Po& operator /=(DB k){x /= k, y /= k;}

    DB length_sqr(){return sqr(x) + sqr(y);}
    DB length(){return sqrt(length_sqr());}

    DB atan(){
        return atan2(y, x);
    }

    void input(){
        int _x, _y; scanf("%d %d", &_x, &_y);
        x = _x, y = _y;
    }
};

bool operator ==(Po a, Po b){return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;}
Po operator +(Po a, Po b){return Po(a.x + b.x, a.y + b.y);}
Po operator -(Po a, Po b){return Po(a.x - b.x, a.y - b.y);}
Po operator *(Po a, DB k){return Po(a.x * k, a.y * k);}
Po operator /(Po a, DB k){return Po(a.x / k, a.y / k);}

struct Line{
    Po a, b;
    Line(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
    Line(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
    Line(Seg);
};

struct Seg{
    Po a, b;
    Seg(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
    Seg(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
    Seg(Line l);

    DB length(){return (b - a).length();}
};

Line::Line(Seg l):a(l.a), b(l.b){}
Seg::Seg(Line l):a(l.a), b(l.b){}

#define innerProduct dot
#define scalarProduct dot
#define dotProduct dot
#define outerProduct det
#define crossProduct det

inline DB dot(DB x1, DB y1, DB x2, DB y2){return x1 * x2 + y1 * y2;}
inline DB dot(Po a, Po b){return dot(a.x, b.y, b.x, b.y);}
inline DB dot(Po p0, Po p1, Po p2){return dot(p1 - p0, p2 - p0);}
inline DB dot(Line l1, Line l2){return dot(l1.b - l1.a, l2.b - l2.a);}
inline DB det(DB x1, DB y1, DB x2, DB y2){return x1 * y2 - x2 * y1;}
inline DB det(Po a, Po b){return det(a.x, a.y, b.x, b.y);}
inline DB det(Po p0, Po p1, Po p2){return det(p1 - p0, p2 - p0);}
inline DB det(Line l1, Line l2){return det(l1.b - l1.a, l2.b - l2.a);}

template<class T1, class T2> inline DB dist(T1 x, T2 y){return sqrt(dist_sqr(x, y));}

inline DB dist_sqr(Po a, Po b){return sqr(a.x - b.x) + sqr(a.y - b.y);}
inline DB dist_sqr(Po p, Line l){Po v0 = l.b - l.a, v1 = p - l.a; return sqr(fabs(det(v0, v1))) / v0.length_sqr();}
inline DB dist_sqr(Po p, Seg l){
    Po v0 = l.b - l.a, v1 = p - l.a, v2 = p - l.b;
    if (sgn(dot(v0, v1)) * sgn(dot(v0, v2)) <= 0) return dist_sqr(p, Line(l));
    else return min(v1.length_sqr(), v2.length_sqr());
}

inline DB dist_sqr(Line l, Po p){
    return dist_sqr(p, l);
}

inline DB dist_sqr(Line l1, Line l2){
    if (sgn(det(l1, l2)) != 0) return 0;
    return dist_sqr(l1.a, l2);
}
inline DB dist_sqr(Line l1, Seg l2){
    Po v0 = l1.b - l1.a, v1 = l2.a - l1.a, v2 = l2.b - l1.a; DB c1 = det(v0, v1), c2 = det(v0, v2);
    return sgn(c1) != sgn(c2) ? 0 : sqr(min(fabs(c1), fabs(c2))) / v0.length_sqr();
}

inline DB dist_sqr(Seg l, Po p){
    return dist_sqr(p, l);
}

inline DB dist_sqr(Seg l1, Line l2){
    return dist_sqr(l2, l1);
}

bool isIntersect(Seg l1, Seg l2){

    //if (l1.a == l2.a || l1.a == l2.b || l1.b == l2.a || l1.b == l2.b) return true;

    return
        min(l1.a.x, l1.b.x) <= max(l2.a.x, l2.b.x) &&
        min(l2.a.x, l2.b.x) <= max(l1.a.x, l1.b.x) &&
        min(l1.a.y, l1.b.y) <= max(l2.a.y, l2.b.y) &&
        min(l2.a.y, l2.b.y) <= max(l1.a.y, l1.b.y) &&
    sgn( det(l1.a, l2.a, l2.b) ) * sgn( det(l1.b, l2.a, l2.b) ) <= 0 &&
    sgn( det(l2.a, l1.a, l1.b) ) * sgn( det(l2.b, l1.a, l1.b) ) <= 0;

}

inline DB dist_sqr(Seg l1, Seg l2){
    if (isIntersect(l1, l2)) return 0;
    else return min(dist_sqr(l1.a, l2), dist_sqr(l1.b, l2), dist_sqr(l2.a, l1), dist_sqr(l2.b, l1));
}

inline bool isOnseg(const Po &p, const Seg &l){
    return sgn(det(p, l.a, l.b)) == 0 &&
        sgn(l.a.x, p.x) * sgn(l.b.x, p.x) <= 0 && sgn(l.a.y, p.y) * sgn(l.b.y, p.y) <= 0;
}

inline Po intersect(const Line &l1, const Line &l2){
    return l1.a + (l1.b - l1.a) * (det(l2.a, l1.a, l2.b) / det(l2, l1));
}

// perpendicular foot
inline Po intersect(const Po & p, const Line &l){
    return intersect(Line(p, p + Po(l.a.y - l.b.y, l.b.x - l.a.x)), l);
}

inline Po rotate(Po p, DB alpha, Po o = Po()){
    p.x -= o.x, p.y -= o .y;
    return Po(p.x * cos(alpha) - p.y * sin(alpha), p.y * cos(alpha) + p.x * sin(alpha)) + o;
}


// <<= ' 0. I/O Accelerator interface .,

template<class T> inline void RD(T &x){
    //cin >> x;
    scanf("%d", &x);
    //char c; for (c = getchar(); c < '0'; c = getchar()); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
    //char c; c = getchar(); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
}

const DB no_solution = -1;

int ____Case;
template<class T> inline void OT(const T &x){
    printf("Case #%d: ", ++____Case);
    printf("%d", x);
    puts("");
}


/* .................................................................................................................................. */


const int N = 50;
bool Map[N][N];
bool exist[100 + 5][100 + 5];

int res;


int main() {

    freopen("D-small-practice.in", "r", stdin);
    freopen("out.txt", "w", stdout);

    int cases, cur;
    int h, w, D;
    int s, px, py, ii, jj, ox, oy, x0, y0;
    double cx, cy, a, b, d;
    bool destroyed;

    Rush{

        RD(h, w, D);
        REP_2(i, j, h, w){
            char t; RC(t); if (t == 'X') x0 = i, y0 = j;
            Map[i][j] = t != '#';
        }

        res = 0;

        int i, j, k;

        for (i=x0-1;Map[i][y0];--i);
        if (((x0-i)<<1)-1<=D) ++res;

        for (i=x0+1;Map[i][y0];++i);
        if (((i-x0)<<1)-1<=D) ++res;

        for (i=y0-1;Map[x0][i];--i);
        if (((y0-i)<<1)-1<=D) ++res;

        for (i=y0+1;Map[x0][i];++i);
        if (((i-y0)<<1)-1<= D) ++res;


		RST(exist);

        FOR(ii, -D+1, D) if (ii) FOR(jj, -D+1, D) if (jj && sqr(ii)+sqr(jj)<=sqr(D)){

            k = abs(__gcd(ii, jj)), i = ii / k, j = jj / k;
            if (exist[i + 50][j + 50]) continue;

            i = ii, j = jj, cx = x0 + 0.5, cy = y0 + 0.5, d = 0, destroyed = false; do{

                if (i < 0) a = (cx - (int)(cx - EPS)) / -i;
                else a = ((int)(cx + 1 + EPS) - cx) / i;

                if (j < 0) b = (cy - (int)(cy - EPS)) / -j;
                else b = ((int)(cy + 1 + EPS) - cy) / j;

                checkMin(a, b);

                if (d + a > 1) break;

                d += a, cx += a * i, cy += a * j;
                px = cx + EPS, py = cy + EPS;

                if (cx - px < EPS && cy - py < EPS) {
                    if (i < 0) ox = px--; else ox = px-1;
                    if (j < 0) oy = py--; else oy = py-1;
                    if (!Map[px]) {
                        destroyed = true;
                        if (!Map[ox]) j = -j, destroyed = false;
                        if (!Map[px][oy]) i = -i, destroyed = false;
                    }
                }
                else if (cx - px < EPS) {
                    if (i < 0) --px;
                    if (!Map[px]) i = -i;
                }
                else if (cy - py < EPS) {
                    if (j < 0) --py;
                    if (!Map[px]) j = -j;
                }

            } while (!destroyed);

            if (destroyed) continue;

            a = (x0 + 0.5 - cx) / i, b = (y0 + 0.5 - cy) / j;
            if (fabs(d + a - 1) < EPS && fabs(d + b - 1) < EPS) {
                k = abs(__gcd(ii, jj)), i = ii / k, j = jj / k;
                ++res, exist[i + 50][j + 50] = true;
            }
        }

        OT(res);
    }
}