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#include <math.h>

#ifdef __GNUC__
#undef gamma
#endif

#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#include <limits.h>
#include <assert.h>
#ifdef __GNUC__
#include <new>
#else
#include <new.h>
#endif

#ifdef NULL
#undef NULL
#endif
#define NULL 0

typedef unsigned char uchar;
typedef unsigned short ushort;
typedef unsigned int uint;

#define max(a,b) (((a) > (b)) ? (a) : (b))
#define min(a,b) (((a) < (b)) ? (a) : (b))
#define rnd(max) (rand()%(max))
#define rndreset() (srand(1))


#define rndtime() { loopi(lastmillis&0xF) rnd(i+1); }

#define loop(v,m) for(int v = 0; v<(m); v++)
#define loopi(m) loop(i,m)
#define loopj(m) loop(j,m)
#define loopk(m) loop(k,m)
#define loopl(m) loop(l,m)

#ifdef WIN32
#pragma warning( 3 : 4189 ) 
//#pragma comment(linker,"/OPT:NOWIN98")
#define PATHDIV '\\'
#else
#define __cdecl
#define _vsnprintf vsnprintf
#define PATHDIV '/'
#endif


// easy safe strings

#define _MAXDEFSTR 260
typedef char string[_MAXDEFSTR]; 


inline void strn0cpy(char *d, const char *s, size_t m) { strncpy(d,s,m); d[(m)-1] = 0; };





inline void strcpy_s(char *d, const char *s) { strn0cpy(d,s,_MAXDEFSTR); };




inline void strcat_s(char *d, const char *s) { size_t n = strlen(d); strn0cpy(d+n,s,_MAXDEFSTR-n); };






inline void formatstring(char *d, const char *fmt, va_list v)
{
    _vsnprintf(d, _MAXDEFSTR, fmt, v);
    d[_MAXDEFSTR-1] = 0;
};

struct sprintf_s_f
{
    char *d;
    sprintf_s_f(char *str): d(str) {};

    void operator()(const char* fmt, ...)
    {
        va_list v;
        va_start(v, fmt);
        _vsnprintf(d, _MAXDEFSTR, fmt, v);
        va_end(v);
        d[_MAXDEFSTR-1] = 0;
    };
};

#define sprintf_s(d) sprintf_s_f((char *)d)
#define sprintf_sd(d) string d; sprintf_s(d)

#define sprintf_sdlv(d,last,fmt) string d; { va_list ap; va_start(ap, last); formatstring(d, fmt, ap); va_end(ap); }
#define sprintf_sdv(d,fmt) sprintf_sdlv(d,fmt,fmt)









// fast pentium f2i

#ifdef _MSC_VER


inline int fast_f2nat(float a) {        // only for positive floats
    static const float fhalf = 0.5f;
    int retval;
    
    __asm fld a
    __asm fsub fhalf
    __asm fistp retval      // perf regalloc?

    return retval;
};
#else
#define fast_f2nat(val) ((int)(val)) 
#endif



extern char *path(char *s);
extern char *loadfile(char *fn, int *size);
extern void endianswap(void *, int, int);

// memory pool that uses buckets and linear allocation for small objects
// VERY fast, and reasonably good memory reuse 

struct pool
{
    enum { POOLSIZE = 4096 };   // can be absolutely anything
    enum { PTRSIZE = sizeof(char *) };


    enum { MAXBUCKETS = 65 };   // meaning up to size 256 on 32bit pointer systems
    enum { MAXREUSESIZE = MAXBUCKETS*PTRSIZE-PTRSIZE };
    inline size_t bucket(size_t s) { return (s+PTRSIZE-1)>>PTRBITS; };




    enum { PTRBITS = PTRSIZE==2 ? 1 : PTRSIZE==4 ? 2 : 3 };

    char *p;
    size_t left;
    char *blocks;
    void *reuse[MAXBUCKETS];

    pool();
    ~pool() { dealloc_block(blocks); };

    void *alloc(size_t size);
    void dealloc(void *p, size_t size);
    void *realloc(void *p, size_t oldsize, size_t newsize);

    char *string(char *s, size_t l);



    char *string(char *s) { return string(s, strlen(s)); };


    void deallocstr(char *s) { dealloc(s, strlen(s)+1); }; 






    char *stringbuf(char *s) { return string(s, _MAXDEFSTR-1); }; 


    void dealloc_block(void *b);
    void allocnext(size_t allocsize);
};

template <class T> struct vector
{
    T *buf;
    int alen;
    int ulen;
    pool *p;

    vector()
    {
        this->p = gp();
        alen = 8;
        buf = (T *)p->alloc(alen*sizeof(T));
        ulen = 0;
    };
    



    ~vector() { setsize(0); p->dealloc(buf, alen*sizeof(T)); };

    
    vector(vector<T> &v);
    void operator=(vector<T> &v);


    T &add(const T &x)
    {

        if(ulen==alen) realloc();
        new (&buf[ulen]) T(x);
        return buf[ulen++];
    };





    T &add()
    {
        if(ulen==alen) realloc();
        new (&buf[ulen]) T;
        return buf[ulen++];
    };




    T &pop() { return buf[--ulen]; };




    T &last() { return buf[ulen-1]; };




    bool empty() { return ulen==0; };





    int length() { return ulen; };


    T &operator[](int i) { assert(i>=0 && i<ulen); return buf[i]; };





    void setsize(int i) { for(; ulen>i; ulen--) buf[ulen-1].~T(); };





    T *getbuf() { return buf; };
    
    void sort(void *cf) { qsort(buf, ulen, sizeof(T), (int (__cdecl *)(const void *,const void *))cf); };



    void realloc()

    {
        int olen = alen;
        buf = (T *)p->realloc(buf, olen*sizeof(T), (alen *= 2)*sizeof(T));

    };










    T remove(int i)
    {
        T e = buf[i];

        for(int p = i+1; p<ulen; p++) buf[p-1] = buf[p];
        ulen--;
        return e;
    };


    T &insert(int i, const T &e)
    {
        add(T());

        for(int p = ulen-1; p>i; p--) buf[p] = buf[p-1];
        buf[i] = e;
        return buf[i];
    };
};




#define loopv(v)    if(false) {} else for(int i = 0; i<(v).length(); i++)    



#define loopvrev(v) if(false) {} else for(int i = (v).length()-1; i>=0; i--)

template <class T> struct hashtable
{
    struct chain { chain *next; char *key; T data; };





    int size;
    int numelems;
    chain **table;
    pool *parent;
    chain *enumc;

    hashtable()
    {
        this->size = 1<<10;
        this->parent = gp();
        numelems = 0;
        table = (chain **)parent->alloc(size*sizeof(T));

        for(int i = 0; i<size; i++) table[i] = NULL;
    };

    hashtable(hashtable<T> &v);
    void operator=(hashtable<T> &v);


    T *access(char *key, T *data = NULL)
    {
        unsigned int h = 5381;
        for(int i = 0, k; k = key[i]; i++) h = ((h<<5)+h)^k;    // bernstein k=33 xor

        h = h&(size-1);                                         // primes not much of an advantage
        for(chain *c = table[h]; c; c = c->next)
        {
            for(char *p1 = key, *p2 = c->key, ch; (ch = *p1++)==*p2++; ) if(!ch)    //if(strcmp(key,c->key)==0)


            {
                T *d = &c->data;

                if(data) c->data = *data;
                return d;
            };
        };
        if(data)
        {
            chain *c = (chain *)parent->alloc(sizeof(chain));
            c->data = *data;
            c->key = key;
            c->next = table[h];
            table[h] = c;
            numelems++;
        };
        return NULL;
    };
};








#define enumerate(ht,t,e,b) loopi(ht->size) for(ht->enumc = ht->table[i]; ht->enumc; ht->enumc = ht->enumc->next) { t e = &ht->enumc->data; b; }

pool *gp(); 



inline char *newstring(char *s)        { return gp()->string(s);    };


inline char *newstring(char *s, size_t l) { return gp()->string(s, l); };






inline char *newstringbuf(char *s)     { return gp()->stringbuf(s); };


#endif








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#include <math.h>

#ifdef __GNUC__
#undef gamma
#endif

#include <assert.h>
#include <limits.h>
#include <stdarg.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#ifdef __GNUC__
#include <new>
#else
#include <new.h>
#endif

#ifdef NULL
#undef NULL
#endif
#define NULL 0

typedef unsigned char uchar;
typedef unsigned short ushort;
typedef unsigned int uint;

#define max(a, b) (((a) > (b)) ? (a) : (b))
#define min(a, b) (((a) < (b)) ? (a) : (b))
#define rnd(max) (rand() % (max))
#define rndreset() (srand(1))
#define rndtime()                                                              \
	{                                                                      \
		loopi(lastmillis & 0xF) rnd(i + 1);                            \
	}
#define loop(v, m) for (int v = 0; v < (m); v++)
#define loopi(m) loop(i, m)
#define loopj(m) loop(j, m)
#define loopk(m) loop(k, m)
#define loopl(m) loop(l, m)

#ifdef WIN32
#pragma warning(3 : 4189)
// #pragma comment(linker,"/OPT:NOWIN98")
#define PATHDIV '\\'
#else
#define __cdecl
#define _vsnprintf vsnprintf
#define PATHDIV '/'
#endif


// easy safe strings

#define _MAXDEFSTR 260
typedef char string[_MAXDEFSTR];

inline void
strn0cpy(char *d, const char *s, size_t m)
{
	strncpy(d, s, m);
	d[(m)-1] = 0;
};
inline void
strcpy_s(char *d, const char *s)
{
	strn0cpy(d, s, _MAXDEFSTR);
};
inline void
strcat_s(char *d, const char *s)
{
	size_t n = strlen(d);
	strn0cpy(d + n, s, _MAXDEFSTR - n);
};

inline void
formatstring(char *d, const char *fmt, va_list v)
{
	_vsnprintf(d, _MAXDEFSTR, fmt, v);
	d[_MAXDEFSTR - 1] = 0;
};

struct sprintf_s_f {

	char *d;
	sprintf_s_f(char *str) : d(str) {};
	void
	operator()(const char *fmt, ...)
	{
		va_list v;
		va_start(v, fmt);
		_vsnprintf(d, _MAXDEFSTR, fmt, v);
		va_end(v);
		d[_MAXDEFSTR - 1] = 0;
	};
};

#define sprintf_s(d) sprintf_s_f((char *)d)
#define sprintf_sd(d)                                                          \
	string d;                                                              \
	sprintf_s(d)
#define sprintf_sdlv(d, last, fmt)                                             \
	string d;                                                              \
	{                                                                      \
		va_list ap;                                                    \
		va_start(ap, last);                                            \
		formatstring(d, fmt, ap);                                      \
		va_end(ap);                                                    \
	}
#define sprintf_sdv(d, fmt) sprintf_sdlv(d, fmt, fmt)

// fast pentium f2i

#ifdef _MSC_VER
inline int
fast_f2nat(float a)
{ // only for positive floats
	static const float fhalf = 0.5f;
	int retval;

	__asm fld a __asm fsub fhalf __asm fistp retval // perf regalloc?



	    return retval;
};
#else
#define fast_f2nat(val) ((int)(val))
#endif



extern char *path(char *s);
extern char *loadfile(char *fn, int *size);
extern void endianswap(void *, int, int);

// memory pool that uses buckets and linear allocation for small objects
// VERY fast, and reasonably good memory reuse

struct pool {

	enum { POOLSIZE = 4096 }; // can be absolutely anything
	enum { PTRSIZE = sizeof(char *) };
	enum {
		MAXBUCKETS = 65
	}; // meaning up to size 256 on 32bit pointer systems
	enum { MAXREUSESIZE = MAXBUCKETS * PTRSIZE - PTRSIZE };
	inline size_t
	bucket(size_t s)
	{
		return (s + PTRSIZE - 1) >> PTRBITS;
	};
	enum { PTRBITS = PTRSIZE == 2 ? 1 : PTRSIZE == 4 ? 2 : 3 };

	char *p;
	size_t left;
	char *blocks;
	void *reuse[MAXBUCKETS];

	pool();
	~pool() { dealloc_block(blocks); };

	void *alloc(size_t size);
	void dealloc(void *p, size_t size);
	void *realloc(void *p, size_t oldsize, size_t newsize);

	char *string(char *s, size_t l);
	char *
	string(char *s)
	{
		return string(s, strlen(s));
	};
	void
	deallocstr(char *s)
	{
		dealloc(s, strlen(s) + 1);
	};
	char *
	stringbuf(char *s)
	{
		return string(s, _MAXDEFSTR - 1);
	};

	void dealloc_block(void *b);
	void allocnext(size_t allocsize);
};

template <class T> struct vector {

	T *buf;
	int alen;
	int ulen;
	pool *p;

	vector()
	{
		this->p = gp();
		alen = 8;
		buf = (T *)p->alloc(alen * sizeof(T));
		ulen = 0;
	};

	~vector()
	{
		setsize(0);
		p->dealloc(buf, alen * sizeof(T));
	};

	vector(vector<T> &v);
	void operator=(vector<T> &v);

	T &
	add(const T &x)
	{
		if (ulen == alen)
			realloc();
		new (&buf[ulen]) T(x);
		return buf[ulen++];
	};

	T &
	add()
	{
		if (ulen == alen)


			realloc();
		new (&buf[ulen]) T;
		return buf[ulen++];
	};

	T &
	pop()
	{
		return buf[--ulen];
	};
	T &
	last()
	{
		return buf[ulen - 1];
	};
	bool
	empty()
	{
		return ulen == 0;
	};

	int
	length()
	{
		return ulen;
	};
	T &
	operator[](int i)
	{
		assert(i >= 0 && i < ulen);
		return buf[i];
	};
	void
	setsize(int i)
	{
		for (; ulen > i; ulen--)
			buf[ulen - 1].~T();
	};
	T *
	getbuf()
	{

		return buf;
	};

	void
	sort(void *cf)
	{

		qsort(buf, ulen, sizeof(T),
		    (int(__cdecl *)(const void *, const void *))cf);
	};

	void
	realloc()
	{
		int olen = alen;
		buf = (T *)p->realloc(
		    buf, olen * sizeof(T), (alen *= 2) * sizeof(T));
	};

	T
	remove(int i)
	{
		T e = buf[i];
		for (int p = i + 1; p < ulen; p++)
			buf[p - 1] = buf[p];
		ulen--;
		return e;
	};

	T &
	insert(int i, const T &e)
	{
		add(T());
		for (int p = ulen - 1; p > i; p--)
			buf[p] = buf[p - 1];
		buf[i] = e;
		return buf[i];
	};
};

#define loopv(v)                                                               \
	if (false) {                                                           \
	} else                                                                 \
		for (int i = 0; i < (v).length(); i++)
#define loopvrev(v)                                                            \
	if (false) {                                                           \
	} else                                                                 \
		for (int i = (v).length() - 1; i >= 0; i--)

template <class T> struct hashtable {

	struct chain {
		chain *next;
		char *key;
		T data;
	};

	int size;
	int numelems;
	chain **table;
	pool *parent;
	chain *enumc;

	hashtable()
	{
		this->size = 1 << 10;
		this->parent = gp();
		numelems = 0;
		table = (chain **)parent->alloc(size * sizeof(T));
		for (int i = 0; i < size; i++)
			table[i] = NULL;
	};

	hashtable(hashtable<T> &v);
	void operator=(hashtable<T> &v);

	T *
	access(char *key, T *data = NULL)
	{
		unsigned int h = 5381;
		for (int i = 0, k; k = key[i]; i++)
			h = ((h << 5) + h) ^ k; // bernstein k=33 xor
		h = h & (size - 1); // primes not much of an advantage
		for (chain *c = table[h]; c; c = c->next) {

			for (char *p1 = key, *p2 = c->key, ch;
			     (ch = *p1++) == *p2++;)
				if (!ch) // if(strcmp(key,c->key)==0)
				{
					T *d = &c->data;
					if (data)
						c->data = *data;
					return d;
				};
		};
		if (data) {

			chain *c = (chain *)parent->alloc(sizeof(chain));
			c->data = *data;
			c->key = key;
			c->next = table[h];
			table[h] = c;
			numelems++;
		};
		return NULL;
	};
};

#define enumerate(ht, t, e, b)                                                 \
	loopi(ht->size) for (ht->enumc = ht->table[i]; ht->enumc;              \
	                     ht->enumc = ht->enumc->next)                      \
	{                                                                      \
		t e = &ht->enumc->data;                                        \
		b;                                                             \
	}


pool *gp();
inline char *
newstring(char *s)
{
	return gp()->string(s);
};
inline char *
newstring(char *s, size_t l)
{
	return gp()->string(s, l);
};
inline char *
newstringbuf(char *s)
{
	return gp()->stringbuf(s);
};

#endif