English
#include <algorithm>
#include <string>
#include <vector>
#include <iostream>
#include <math.h>
#include <stdint.h>
#include <limits.h>
#include <vector>
#include <algorithm>
#include <iostream>
using namespace std;
// Klasa Num skopiowana z: https://github.com/983/Num
// Licencja: http://unlicense.org
class Num {
public:
typedef uint64_t word;
std::vector<word> words;
bool neg;
static word word_mask(){
return (word)-1;
}
static size_t word_bits(){
return sizeof(word)*CHAR_BIT;
}
static word word_half_mask(){
return word_mask() >> word_bits()/2;
}
static word char_to_word(char c){
switch (c){
case '0': return 0;
case '1': return 1;
case '2': return 2;
case '3': return 3;
case '4': return 4;
case '5': return 5;
case '6': return 6;
case '7': return 7;
case '8': return 8;
case '9': return 9;
case 'a': case 'A': return 10;
case 'b': case 'B': return 11;
case 'c': case 'C': return 12;
case 'd': case 'D': return 13;
case 'e': case 'E': return 14;
case 'f': case 'F': return 15;
case 'g': case 'G': return 16;
case 'h': case 'H': return 17;
case 'i': case 'I': return 18;
case 'j': case 'J': return 19;
case 'k': case 'K': return 20;
case 'l': case 'L': return 21;
case 'm': case 'M': return 22;
case 'n': case 'N': return 23;
case 'o': case 'O': return 24;
case 'p': case 'P': return 25;
case 'q': case 'Q': return 26;
case 'r': case 'R': return 27;
case 's': case 'S': return 28;
case 't': case 'T': return 29;
case 'u': case 'U': return 30;
case 'v': case 'V': return 31;
case 'w': case 'W': return 32;
case 'x': case 'X': return 33;
case 'y': case 'Y': return 34;
case 'z': case 'Z': return 35;
default: return word_mask();
}
}
static word word_gcd(word a, word b){
while (1){
if (a == 0) return b;
b %= a;
if (b == 0) return a;
a %= b;
}
}
Num(): neg(false){}
Num(size_t n, word w, bool neg = false): words(n, w), neg(neg){}
Num(const word *a, const word *b, bool neg = false) : words(a, b), neg(neg){
truncate();
}
Num(const Num &a){
words = a.words;
neg = a.neg;
}
Num& operator = (const Num &a){
words = a.words;
neg = a.neg;
return *this;
}
Num(int i): neg(i < 0){
unsigned u = (i < 0) ? -(unsigned)i : (unsigned)i;
if (sizeof(u) <= word_bits()){
if (u > 0) push_back(u);
}else{
for (; u; u >>= word_bits()) push_back(u);
}
}
Num(const char *c, word base = 10, char **endptr = NULL): neg(false){
// read sign
if (*c == '-'){
c++;
neg = true;
}
// read digits
for (;*c; c++){
mul_word(base);
word b = char_to_word(*c);
if (b >= base) break;
add_word(b);
}
if (endptr) *endptr = (char*)c;
}
void resize(size_t n){
words.resize(n);
}
void pop_back(){
words.pop_back();
}
void push_back(word b){
words.push_back(b);
}
word& back(){
return words.back();
}
const word& back() const {
return words.back();
}
size_t size() const {
return words.size();
}
word& operator [] (size_t i){
return words[i];
}
const word& operator [] (size_t i) const {
return words[i];
}
Num& set_neg(bool neg){
this->neg = neg;
return *this;
}
Num& truncate(){
while (size() > 0 && words.back() == 0) pop_back();
return *this;
}
size_t bitlength() const {
if (size() == 0) return 0;
size_t last = size() - 1;
size_t result = word_bitlength((*this)[last]) + last*word_bits();
return result;
}
size_t count_trailing_zeros() const {
for (size_t i = 0; i < size(); i++){
word w = (*this)[i];
if (w) return word_count_trailing_zeros(w) + i*word_bits();
}
return 0;
}
static int cmp_abs(const Num &a, const Num &b){
size_t na = a.size(), nb = b.size();
if (na != nb){
return na < nb ? -1 : +1;
}
for (size_t i = na; i --> 0;){
word wa = a[i], wb = b[i];
if (wa != wb){
return wa < wb ? -1 : +1;
}
}
return 0;
}
static int cmp(const Num &a, const Num &b){
if (a.size() == 0 && b.size() == 0) return 0;
if (!a.neg && !b.neg) return +cmp_abs(a, b);
if ( a.neg && b.neg) return -cmp_abs(a, b);
return a.neg && !b.neg ? -1 : +1;
}
static size_t word_bitlength(word a){
for (int i = word_bits() - 1; i >= 0; i--) if ((a >> i) & 1) return i+1;
return 0;
}
static size_t word_count_trailing_zeros(word a){
for (int i = 0; i < (int)word_bits(); i++) if ((a >> i) & 1) return i;
return word_bits();
}
static word add_carry(word *a, word b){
return (*a += b) < b;
}
static word sub_carry(word *a, word b){
word tmp = *a;
return (*a = tmp - b) > tmp;
}
static word word_mul_hi(word a, word b){
size_t n = word_bits()/2;
word a_hi = a >> n;
word a_lo = a & word_half_mask();
word b_hi = b >> n;
word b_lo = b & word_half_mask();
word tmp = ((a_lo*b_lo) >> n) + a_hi*b_lo;
tmp = (tmp >> n) + ((a_lo*b_hi + (tmp & word_half_mask())) >> n);
return tmp + a_hi*b_hi;
}
static Num& add_unsigned_overwrite(Num &a, const Num &b){
size_t i, na = a.size(), nb = b.size(), n = std::max(na, nb);
a.resize(n);
word carry = 0;
for (i = 0; i < nb; i++){
carry = add_carry(&a[i], carry);
carry += add_carry(&a[i], b[i]);
}
for (; i < n && carry; i++) carry = add_carry(&a[i], carry);
if (carry) a.push_back(carry);
return a.truncate();
}
static Num& sub_unsigned_overwrite(Num &a, const Num &b){
//assert(cmp_abs(a, b) >= 0);
size_t i, na = a.size(), nb = b.size();
word carry = 0;
for (i = 0; i < nb; i++){
carry = sub_carry(&a[i], carry);
carry += sub_carry(&a[i], b[i]);
}
for (; i < na && carry; i++) carry = sub_carry(&a[i], carry);
//assert(!carry);
return a.truncate();
}
static Num mul_long(const Num &a, const Num &b){
size_t na = a.size(), nb = b.size(), nc = na + nb + 1;
Num c(nc, 0, a.neg ^ b.neg), carries(nc, 0);
for (size_t ia = 0; ia < na; ia++){
for (size_t ib = 0; ib < nb; ib++){
size_t i = ia + ib, j = i + 1;
// WARNING: Might overflow if word size is chosen too small
carries[i + 1] += add_carry(&c[i], a[ia] * b[ib]);
carries[j + 1] += add_carry(&c[j], word_mul_hi(a[ia], b[ib]));
}
}
return add_unsigned_overwrite(c, carries).truncate();
}
static Num mul_karatsuba(const Num &a, const Num &b){
size_t na = a.size(), nb = b.size(), n = std::max(na, nb), m2 = n/2 + (n & 1);
Num a_parts[2], b_parts[2];
split(a, a_parts, 2, m2);
split(b, b_parts, 2, m2);
m2 *= word_bits();
Num z0 = a_parts[0] * b_parts[0];
Num z1 = (a_parts[0] + a_parts[1]) * (b_parts[0] + b_parts[1]);
Num z2 = a_parts[1] * b_parts[1];
Num result = z2;
result <<= m2;
result += z1 - z2 - z0;
result <<= m2;
result += z0;
return result;
}
static Num mul(const Num &a, const Num &b){
size_t karatsuba_threshold = 20;
if (a.size() > karatsuba_threshold && b.size() > karatsuba_threshold){
return mul_karatsuba(a, b);
}
return mul_long(a, b);
}
static Num add_signed(const Num &a, bool a_neg, const Num &b, bool b_neg){
if (a_neg == b_neg) return add_unsigned(a, b).set_neg(a_neg);
if (cmp_abs(a, b) >= 0) return sub_unsigned(a, b).set_neg(a_neg);
return sub_unsigned(b, a).set_neg(b_neg);
}
Num& operator >>= (size_t n_bits){
if (n_bits == 0) return *this;
size_t n_words = n_bits / word_bits();
if (n_words >= size()){
resize(0);
return *this;
}
n_bits %= word_bits();
if (n_bits == 0){
for (size_t i = 0; i < size() - n_words; i++){
(*this)[i] = (*this)[i + n_words];
}
}else{
word hi, lo = (*this)[n_words];
for (size_t i = 0; i < size() - n_words - 1; i++){
hi = (*this)[i + n_words + 1];
(*this)[i] = (hi << (word_bits() - n_bits)) | (lo >> n_bits);
lo = hi;
}
(*this)[size() - n_words - 1] = lo >> n_bits;
}
resize(size() - n_words);
return truncate();
}
Num& operator <<= (size_t n_bits){
if (n_bits == 0) return *this;
size_t n_words = n_bits / word_bits();
n_bits %= word_bits();
size_t old_size = size();
size_t n = old_size + n_words + (n_bits != 0);
resize(n);
if (n_bits == 0){
for (size_t i = n; i --> n_words;){
(*this)[i] = (*this)[i - n_words];
}
}else{
word lo, hi = 0;
for (size_t i = n - 1; i > n_words; i--){
lo = (*this)[i - n_words - 1];
(*this)[i] = (hi << n_bits) | (lo >> (word_bits() - n_bits));
hi = lo;
}
(*this)[n_words] = hi << n_bits;
}
for (size_t i = 0; i < n_words; i++) (*this)[i] = 0;
return truncate();
}
static void div_mod(const Num &numerator, Num denominator, Num "ient, Num &remainder){
quotient = 0;
remainder = numerator;
if (cmp_abs(remainder, denominator) >= 0){
int n = numerator.bitlength() - denominator.bitlength();
denominator <<= n;
for (; n >= 0; n--){
if (cmp_abs(remainder, denominator) >= 0){
sub_unsigned_overwrite(remainder, denominator);
quotient.set_bit(n);
}
denominator >>= 1;
}
}
quotient.set_neg(numerator.neg ^ denominator.neg);
remainder.set_neg(numerator.neg);
}
static void div_mod_half_word(const Num &numerator, word denominator, Num "ient, word &remainder){
remainder = 0;
Num dst(numerator.size(), 0);
for (size_t i = numerator.size(); i --> 0;){
word dst_word = 0;
word src_word = numerator[i];
word parts[2];
parts[0] = src_word >> word_bits()/2;
parts[1] = src_word & word_half_mask();
for (size_t j = 0; j < 2; j++){
remainder <<= word_bits()/2;
remainder |= parts[j];
word div_word = remainder / denominator;
word mod_word = remainder % denominator;
remainder = mod_word;
dst_word <<= word_bits()/2;
dst_word |= div_word;
}
dst[i] = dst_word;
}
quotient = dst.truncate().set_neg(numerator.neg);
}
static void split(const Num &a, Num *parts, size_t n_parts, size_t n){
size_t i = 0;
for (size_t k = 0; k < n_parts; k++){
Num &part = parts[k];
part.resize(n);
for (size_t j = 0; j < n && i < a.size(); j++) part[j] = a[i++];
part = part.truncate();
}
}
static Num div(const Num &numerator, const Num& denominator){
Num quotient, remainder;
div_mod(numerator, denominator, quotient, remainder);
return quotient;
}
static Num mod(const Num &numerator, const Num& denominator){
Num quotient, remainder;
div_mod(numerator, denominator, quotient, remainder);
return remainder;
}
static Num add_unsigned(const Num &a, const Num &b){
Num result(a);
return add_unsigned_overwrite(result, b);
}
static Num sub_unsigned(const Num &a, const Num &b){
Num result(a);
return sub_unsigned_overwrite(result, b);
}
static Num add(const Num &a, const Num &b){
Num result = add_signed(a, a.neg, b, b.neg);
return result;
}
static Num sub(const Num &a, const Num &b){
Num result = add_signed(a, a.neg, b, !b.neg);
return result;
}
static Num gcd(const Num &a0, const Num &b0){
if (a0.size() == 1 && b0.size() == 1){
return Num(1, word_gcd(a0[0], b0[0]));
}
Num a(a0), b(b0);
a.neg = b.neg = false;
if (a.size() == 0) return b0;
if (b.size() == 0) return a0;
size_t n = a.count_trailing_zeros();
size_t m = b.count_trailing_zeros();
if (n > m) {
std::swap(n, m);
a.words.swap(b.words);
}
a >>= n;
b >>= n;
do {
b >>= b.count_trailing_zeros();
if (cmp_abs(a, b) > 0) a.words.swap(b.words);
sub_unsigned_overwrite(b, a);
} while (b.size() > 0);
a <<= n;
return a;
}
typedef void (*random_func)(uint8_t *bytes, size_t n_bytes);
static Num random_bits(size_t n_bits, random_func func){
if (n_bits == 0) return 0;
size_t partial_bits = n_bits % word_bits();
size_t n_words = n_bits / word_bits() + (partial_bits > 0);
size_t n_bytes = n_words*sizeof(word);
Num result(n_words, 0);
uint8_t *bytes = (uint8_t*)&result[0];
func(bytes, n_bytes);
if (partial_bits){
size_t too_many_bits = word_bits() - partial_bits;
result.back() >>= too_many_bits;
}
return result;
}
static Num random_inclusive(const Num &inclusive, random_func func){
size_t n_bits = inclusive.bitlength();
while (true){
Num result = random_bits(n_bits, func);
if (result <= inclusive) return result;
}
}
static Num random_exclusive(const Num &exclusive, random_func func){
size_t n_bits = exclusive.bitlength();
while (true){
Num result = random_bits(n_bits, func);
if (result < exclusive) return result;
}
}
static Num random_second_exclusive(const Num &inclusive_min_val, const Num &exclusive_max_val, random_func func){
return inclusive_min_val + random_exclusive(exclusive_max_val - inclusive_min_val, func);
}
static Num random_both_inclusive(const Num &inclusive_min_val, const Num &inclusive_max_val, random_func func){
return inclusive_min_val + random_inclusive(inclusive_max_val - inclusive_min_val, func);
}
Num& set_bit(size_t i){
size_t i_word = i / word_bits();
size_t i_bit = i % word_bits();
if (size() <= i_word) resize(i_word + 1);
(*this)[i_word] |= ((word)1) << i_bit;
return *this;
}
word get_bit(size_t i) const {
size_t i_word = i / word_bits();
size_t i_bit = i % word_bits();
if (i_word >= size()) return 0;
return ((*this)[i_word] >> i_bit) & 1;
}
void clr_bit(size_t i){
size_t i_word = i / word_bits();
size_t i_bit = i % word_bits();
if (i_word >= size()) return;
word mask = 1;
mask <<= i_bit;
(*this)[i_word] &= ~mask;
}
Num& mul_word(word b){
word carry = 0;
for (size_t i = 0; i < size(); i++){
word a = (*this)[i];
word tmp = a * b;
carry = add_carry(&tmp, carry);
carry += word_mul_hi(a, b);
(*this)[i] = tmp;
}
if (carry) push_back(carry);
return truncate();
}
Num& add_word(word carry, size_t i0 = 0){
if (i0 >= size()) resize(i0 + 1);
for (size_t i = i0; i < size() && carry; i++){
carry = add_carry(&(*this)[i], carry);
}
if (carry) push_back(carry);
return truncate();
}
void print(
std::vector<char> &text,
word base = 10,
const char *alphabet = "0123456789abcdefghijklmnopqrstuvwxyz"
) const {
if (size() == 0){
text.push_back('0');
}else{
Num tmp(*this);
while (tmp.size() > 0){
word remainder;
div_mod_half_word(tmp, base, tmp, remainder);
text.push_back(alphabet[remainder]);
}
if (neg) text.push_back('-');
std::reverse(text.begin(), text.end());
}
text.push_back('\0');
}
friend std::ostream& operator << (std::ostream& out, const Num &num){
std::vector<char> tmp;
num.print(tmp);
out << &tmp[0];
return out;
}
double to_double() const {
if (size() == 0) return 0.0;
double d = 0.0, base = ::pow(2.0, word_bits());
for (size_t i = size(); i --> 0;) d = d * base + (*this)[i];
return neg ? -d : d;
}
bool can_convert_to_int(int *result){
if (*this < Num(INT_MIN) || *this > Num(INT_MAX)) return false;
unsigned temp = 0;
if (word_bits() >= sizeof(temp)*CHAR_BIT){
if (words.size() > 0){
temp = (*this)[0];
}
}else{
for (size_t i = words.size(); i --> 0;){
temp <<= word_bits();
temp += (*this)[i];
}
}
*result = neg ? -temp : temp;
return true;
}
Num pow(size_t exponent) const {
Num result(1), p(*this);
for (; exponent; exponent >>= 1){
if (exponent & 1){
result = result * p;
exponent--;
}
p = p*p;
}
return result;
}
Num mod_pow(Num exponent, const Num &modulus) const {
Num result(1), base = (*this) % modulus;
for (; exponent.size() > 0; exponent >>= 1){
if (exponent.get_bit(0)){
result = (result * base) % modulus;
}
base = (base * base) % modulus;
}
return result;
}
Num sqrt() const {
Num n = *this;
int bit = bitlength();
if (bit & 1) bit ^= 1;
Num result = 0;
for (; bit >= 0; bit -= 2){
Num tmp = result;
tmp.set_bit(bit);
if (n >= tmp){
n -= tmp;
result.set_bit(bit + 1);
}
result >>= 1;
}
return result;
}
Num& operator ++(){
add_word(1);
return *this;
}
Num& operator += (const Num &b){ return *this = add(*this, b); }
Num& operator -= (const Num &b){ return *this = sub(*this, b); }
Num& operator *= (const Num &b){ return *this = mul(*this, b); }
Num& operator /= (const Num &b){ return *this = div(*this, b); }
Num& operator %= (const Num &b){ return *this = mod(*this, b); }
bool operator == (const Num &b) const { return cmp(*this, b) == 0; }
bool operator != (const Num &b) const { return cmp(*this, b) != 0; }
bool operator <= (const Num &b) const { return cmp(*this, b) <= 0; }
bool operator >= (const Num &b) const { return cmp(*this, b) >= 0; }
bool operator < (const Num &b) const { return cmp(*this, b) < 0; }
bool operator > (const Num &b) const { return cmp(*this, b) > 0; }
Num operator + (const Num &b) const { return add(*this, b); }
Num operator - (const Num &b) const { return sub(*this, b); }
Num operator * (const Num &b) const { return mul(*this, b); }
Num operator / (const Num &b) const { return div(*this, b); }
Num operator % (const Num &b) const { return mod(*this, b); }
Num operator - ( ) const { return Num(*this).set_neg(!neg); }
Num operator >> (size_t n_bits) const { return Num(*this) >>= n_bits; }
Num operator << (size_t n_bits) const { return Num(*this) <<= n_bits; }
};
int st[200];
typedef Num LL;
vector<int> nast[200], skad[200];
int n;
LL wyn=1;
LL wyl[200], wym[200];
void dostepny(int x)
{
if (st[x])
return;
st[x]=1;
for (int i : nast[x])
dostepny(i);
}
LL nwd(LL a, LL b)
{
while (b!=0)
{
LL x=b;
b=a%b;
a=x;
}
return a;
}
LL nww(LL a, LL b)
{
return a/nwd(a, b)*b;
}
void oblicz(int x)
{
if (st[x]!=1 || nast[x].empty())
return;
LL l=0, m=1;
if (x==1)
l=1;
else
{
for (int i : skad[x])
{
if (st[i]==0)
continue;
oblicz(i);
LL ll=l*wym[i]+wyl[i]*m;
LL mm=m*wym[i];
LL s=nwd(ll, mm);
l=ll/s;
m=mm/s;
}
}
m*=nast[x].size();
st[x]=2;
LL w=m/nwd(nast[x].size(), l);
wyn=nww(wyn, w);
LL s=nwd(l, m);
wyl[x]=l/s;
wym[x]=m/s;
}
int main()
{
ios_base::sync_with_stdio(false);
cin>>n;
for (int i=1; i<=n; ++i)
{
int r;
cin>>r;
for (int j=0; j<r; ++j)
{
int a;
cin>>a;
nast[i].push_back(a);
skad[a].push_back(i);
}
}
dostepny(1);
for (int i=1; i<=n; ++i)
oblicz(i);
cout<<wyn<<endl;
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 | #include <algorithm> #include <string> #include <vector> #include <iostream> #include <math.h> #include <stdint.h> #include <limits.h> #include <vector> #include <algorithm> #include <iostream> using namespace std; // Klasa Num skopiowana z: https://github.com/983/Num // Licencja: http://unlicense.org class Num { public: typedef uint64_t word; std::vector<word> words; bool neg; static word word_mask(){ return (word)-1; } static size_t word_bits(){ return sizeof(word)*CHAR_BIT; } static word word_half_mask(){ return word_mask() >> word_bits()/2; } static word char_to_word(char c){ switch (c){ case '0': return 0; case '1': return 1; case '2': return 2; case '3': return 3; case '4': return 4; case '5': return 5; case '6': return 6; case '7': return 7; case '8': return 8; case '9': return 9; case 'a': case 'A': return 10; case 'b': case 'B': return 11; case 'c': case 'C': return 12; case 'd': case 'D': return 13; case 'e': case 'E': return 14; case 'f': case 'F': return 15; case 'g': case 'G': return 16; case 'h': case 'H': return 17; case 'i': case 'I': return 18; case 'j': case 'J': return 19; case 'k': case 'K': return 20; case 'l': case 'L': return 21; case 'm': case 'M': return 22; case 'n': case 'N': return 23; case 'o': case 'O': return 24; case 'p': case 'P': return 25; case 'q': case 'Q': return 26; case 'r': case 'R': return 27; case 's': case 'S': return 28; case 't': case 'T': return 29; case 'u': case 'U': return 30; case 'v': case 'V': return 31; case 'w': case 'W': return 32; case 'x': case 'X': return 33; case 'y': case 'Y': return 34; case 'z': case 'Z': return 35; default: return word_mask(); } } static word word_gcd(word a, word b){ while (1){ if (a == 0) return b; b %= a; if (b == 0) return a; a %= b; } } Num(): neg(false){} Num(size_t n, word w, bool neg = false): words(n, w), neg(neg){} Num(const word *a, const word *b, bool neg = false) : words(a, b), neg(neg){ truncate(); } Num(const Num &a){ words = a.words; neg = a.neg; } Num& operator = (const Num &a){ words = a.words; neg = a.neg; return *this; } Num(int i): neg(i < 0){ unsigned u = (i < 0) ? -(unsigned)i : (unsigned)i; if (sizeof(u) <= word_bits()){ if (u > 0) push_back(u); }else{ for (; u; u >>= word_bits()) push_back(u); } } Num(const char *c, word base = 10, char **endptr = NULL): neg(false){ // read sign if (*c == '-'){ c++; neg = true; } // read digits for (;*c; c++){ mul_word(base); word b = char_to_word(*c); if (b >= base) break; add_word(b); } if (endptr) *endptr = (char*)c; } void resize(size_t n){ words.resize(n); } void pop_back(){ words.pop_back(); } void push_back(word b){ words.push_back(b); } word& back(){ return words.back(); } const word& back() const { return words.back(); } size_t size() const { return words.size(); } word& operator [] (size_t i){ return words[i]; } const word& operator [] (size_t i) const { return words[i]; } Num& set_neg(bool neg){ this->neg = neg; return *this; } Num& truncate(){ while (size() > 0 && words.back() == 0) pop_back(); return *this; } size_t bitlength() const { if (size() == 0) return 0; size_t last = size() - 1; size_t result = word_bitlength((*this)[last]) + last*word_bits(); return result; } size_t count_trailing_zeros() const { for (size_t i = 0; i < size(); i++){ word w = (*this)[i]; if (w) return word_count_trailing_zeros(w) + i*word_bits(); } return 0; } static int cmp_abs(const Num &a, const Num &b){ size_t na = a.size(), nb = b.size(); if (na != nb){ return na < nb ? -1 : +1; } for (size_t i = na; i --> 0;){ word wa = a[i], wb = b[i]; if (wa != wb){ return wa < wb ? -1 : +1; } } return 0; } static int cmp(const Num &a, const Num &b){ if (a.size() == 0 && b.size() == 0) return 0; if (!a.neg && !b.neg) return +cmp_abs(a, b); if ( a.neg && b.neg) return -cmp_abs(a, b); return a.neg && !b.neg ? -1 : +1; } static size_t word_bitlength(word a){ for (int i = word_bits() - 1; i >= 0; i--) if ((a >> i) & 1) return i+1; return 0; } static size_t word_count_trailing_zeros(word a){ for (int i = 0; i < (int)word_bits(); i++) if ((a >> i) & 1) return i; return word_bits(); } static word add_carry(word *a, word b){ return (*a += b) < b; } static word sub_carry(word *a, word b){ word tmp = *a; return (*a = tmp - b) > tmp; } static word word_mul_hi(word a, word b){ size_t n = word_bits()/2; word a_hi = a >> n; word a_lo = a & word_half_mask(); word b_hi = b >> n; word b_lo = b & word_half_mask(); word tmp = ((a_lo*b_lo) >> n) + a_hi*b_lo; tmp = (tmp >> n) + ((a_lo*b_hi + (tmp & word_half_mask())) >> n); return tmp + a_hi*b_hi; } static Num& add_unsigned_overwrite(Num &a, const Num &b){ size_t i, na = a.size(), nb = b.size(), n = std::max(na, nb); a.resize(n); word carry = 0; for (i = 0; i < nb; i++){ carry = add_carry(&a[i], carry); carry += add_carry(&a[i], b[i]); } for (; i < n && carry; i++) carry = add_carry(&a[i], carry); if (carry) a.push_back(carry); return a.truncate(); } static Num& sub_unsigned_overwrite(Num &a, const Num &b){ //assert(cmp_abs(a, b) >= 0); size_t i, na = a.size(), nb = b.size(); word carry = 0; for (i = 0; i < nb; i++){ carry = sub_carry(&a[i], carry); carry += sub_carry(&a[i], b[i]); } for (; i < na && carry; i++) carry = sub_carry(&a[i], carry); //assert(!carry); return a.truncate(); } static Num mul_long(const Num &a, const Num &b){ size_t na = a.size(), nb = b.size(), nc = na + nb + 1; Num c(nc, 0, a.neg ^ b.neg), carries(nc, 0); for (size_t ia = 0; ia < na; ia++){ for (size_t ib = 0; ib < nb; ib++){ size_t i = ia + ib, j = i + 1; // WARNING: Might overflow if word size is chosen too small carries[i + 1] += add_carry(&c[i], a[ia] * b[ib]); carries[j + 1] += add_carry(&c[j], word_mul_hi(a[ia], b[ib])); } } return add_unsigned_overwrite(c, carries).truncate(); } static Num mul_karatsuba(const Num &a, const Num &b){ size_t na = a.size(), nb = b.size(), n = std::max(na, nb), m2 = n/2 + (n & 1); Num a_parts[2], b_parts[2]; split(a, a_parts, 2, m2); split(b, b_parts, 2, m2); m2 *= word_bits(); Num z0 = a_parts[0] * b_parts[0]; Num z1 = (a_parts[0] + a_parts[1]) * (b_parts[0] + b_parts[1]); Num z2 = a_parts[1] * b_parts[1]; Num result = z2; result <<= m2; result += z1 - z2 - z0; result <<= m2; result += z0; return result; } static Num mul(const Num &a, const Num &b){ size_t karatsuba_threshold = 20; if (a.size() > karatsuba_threshold && b.size() > karatsuba_threshold){ return mul_karatsuba(a, b); } return mul_long(a, b); } static Num add_signed(const Num &a, bool a_neg, const Num &b, bool b_neg){ if (a_neg == b_neg) return add_unsigned(a, b).set_neg(a_neg); if (cmp_abs(a, b) >= 0) return sub_unsigned(a, b).set_neg(a_neg); return sub_unsigned(b, a).set_neg(b_neg); } Num& operator >>= (size_t n_bits){ if (n_bits == 0) return *this; size_t n_words = n_bits / word_bits(); if (n_words >= size()){ resize(0); return *this; } n_bits %= word_bits(); if (n_bits == 0){ for (size_t i = 0; i < size() - n_words; i++){ (*this)[i] = (*this)[i + n_words]; } }else{ word hi, lo = (*this)[n_words]; for (size_t i = 0; i < size() - n_words - 1; i++){ hi = (*this)[i + n_words + 1]; (*this)[i] = (hi << (word_bits() - n_bits)) | (lo >> n_bits); lo = hi; } (*this)[size() - n_words - 1] = lo >> n_bits; } resize(size() - n_words); return truncate(); } Num& operator <<= (size_t n_bits){ if (n_bits == 0) return *this; size_t n_words = n_bits / word_bits(); n_bits %= word_bits(); size_t old_size = size(); size_t n = old_size + n_words + (n_bits != 0); resize(n); if (n_bits == 0){ for (size_t i = n; i --> n_words;){ (*this)[i] = (*this)[i - n_words]; } }else{ word lo, hi = 0; for (size_t i = n - 1; i > n_words; i--){ lo = (*this)[i - n_words - 1]; (*this)[i] = (hi << n_bits) | (lo >> (word_bits() - n_bits)); hi = lo; } (*this)[n_words] = hi << n_bits; } for (size_t i = 0; i < n_words; i++) (*this)[i] = 0; return truncate(); } static void div_mod(const Num &numerator, Num denominator, Num "ient, Num &remainder){ quotient = 0; remainder = numerator; if (cmp_abs(remainder, denominator) >= 0){ int n = numerator.bitlength() - denominator.bitlength(); denominator <<= n; for (; n >= 0; n--){ if (cmp_abs(remainder, denominator) >= 0){ sub_unsigned_overwrite(remainder, denominator); quotient.set_bit(n); } denominator >>= 1; } } quotient.set_neg(numerator.neg ^ denominator.neg); remainder.set_neg(numerator.neg); } static void div_mod_half_word(const Num &numerator, word denominator, Num "ient, word &remainder){ remainder = 0; Num dst(numerator.size(), 0); for (size_t i = numerator.size(); i --> 0;){ word dst_word = 0; word src_word = numerator[i]; word parts[2]; parts[0] = src_word >> word_bits()/2; parts[1] = src_word & word_half_mask(); for (size_t j = 0; j < 2; j++){ remainder <<= word_bits()/2; remainder |= parts[j]; word div_word = remainder / denominator; word mod_word = remainder % denominator; remainder = mod_word; dst_word <<= word_bits()/2; dst_word |= div_word; } dst[i] = dst_word; } quotient = dst.truncate().set_neg(numerator.neg); } static void split(const Num &a, Num *parts, size_t n_parts, size_t n){ size_t i = 0; for (size_t k = 0; k < n_parts; k++){ Num &part = parts[k]; part.resize(n); for (size_t j = 0; j < n && i < a.size(); j++) part[j] = a[i++]; part = part.truncate(); } } static Num div(const Num &numerator, const Num& denominator){ Num quotient, remainder; div_mod(numerator, denominator, quotient, remainder); return quotient; } static Num mod(const Num &numerator, const Num& denominator){ Num quotient, remainder; div_mod(numerator, denominator, quotient, remainder); return remainder; } static Num add_unsigned(const Num &a, const Num &b){ Num result(a); return add_unsigned_overwrite(result, b); } static Num sub_unsigned(const Num &a, const Num &b){ Num result(a); return sub_unsigned_overwrite(result, b); } static Num add(const Num &a, const Num &b){ Num result = add_signed(a, a.neg, b, b.neg); return result; } static Num sub(const Num &a, const Num &b){ Num result = add_signed(a, a.neg, b, !b.neg); return result; } static Num gcd(const Num &a0, const Num &b0){ if (a0.size() == 1 && b0.size() == 1){ return Num(1, word_gcd(a0[0], b0[0])); } Num a(a0), b(b0); a.neg = b.neg = false; if (a.size() == 0) return b0; if (b.size() == 0) return a0; size_t n = a.count_trailing_zeros(); size_t m = b.count_trailing_zeros(); if (n > m) { std::swap(n, m); a.words.swap(b.words); } a >>= n; b >>= n; do { b >>= b.count_trailing_zeros(); if (cmp_abs(a, b) > 0) a.words.swap(b.words); sub_unsigned_overwrite(b, a); } while (b.size() > 0); a <<= n; return a; } typedef void (*random_func)(uint8_t *bytes, size_t n_bytes); static Num random_bits(size_t n_bits, random_func func){ if (n_bits == 0) return 0; size_t partial_bits = n_bits % word_bits(); size_t n_words = n_bits / word_bits() + (partial_bits > 0); size_t n_bytes = n_words*sizeof(word); Num result(n_words, 0); uint8_t *bytes = (uint8_t*)&result[0]; func(bytes, n_bytes); if (partial_bits){ size_t too_many_bits = word_bits() - partial_bits; result.back() >>= too_many_bits; } return result; } static Num random_inclusive(const Num &inclusive, random_func func){ size_t n_bits = inclusive.bitlength(); while (true){ Num result = random_bits(n_bits, func); if (result <= inclusive) return result; } } static Num random_exclusive(const Num &exclusive, random_func func){ size_t n_bits = exclusive.bitlength(); while (true){ Num result = random_bits(n_bits, func); if (result < exclusive) return result; } } static Num random_second_exclusive(const Num &inclusive_min_val, const Num &exclusive_max_val, random_func func){ return inclusive_min_val + random_exclusive(exclusive_max_val - inclusive_min_val, func); } static Num random_both_inclusive(const Num &inclusive_min_val, const Num &inclusive_max_val, random_func func){ return inclusive_min_val + random_inclusive(inclusive_max_val - inclusive_min_val, func); } Num& set_bit(size_t i){ size_t i_word = i / word_bits(); size_t i_bit = i % word_bits(); if (size() <= i_word) resize(i_word + 1); (*this)[i_word] |= ((word)1) << i_bit; return *this; } word get_bit(size_t i) const { size_t i_word = i / word_bits(); size_t i_bit = i % word_bits(); if (i_word >= size()) return 0; return ((*this)[i_word] >> i_bit) & 1; } void clr_bit(size_t i){ size_t i_word = i / word_bits(); size_t i_bit = i % word_bits(); if (i_word >= size()) return; word mask = 1; mask <<= i_bit; (*this)[i_word] &= ~mask; } Num& mul_word(word b){ word carry = 0; for (size_t i = 0; i < size(); i++){ word a = (*this)[i]; word tmp = a * b; carry = add_carry(&tmp, carry); carry += word_mul_hi(a, b); (*this)[i] = tmp; } if (carry) push_back(carry); return truncate(); } Num& add_word(word carry, size_t i0 = 0){ if (i0 >= size()) resize(i0 + 1); for (size_t i = i0; i < size() && carry; i++){ carry = add_carry(&(*this)[i], carry); } if (carry) push_back(carry); return truncate(); } void print( std::vector<char> &text, word base = 10, const char *alphabet = "0123456789abcdefghijklmnopqrstuvwxyz" ) const { if (size() == 0){ text.push_back('0'); }else{ Num tmp(*this); while (tmp.size() > 0){ word remainder; div_mod_half_word(tmp, base, tmp, remainder); text.push_back(alphabet[remainder]); } if (neg) text.push_back('-'); std::reverse(text.begin(), text.end()); } text.push_back('\0'); } friend std::ostream& operator << (std::ostream& out, const Num &num){ std::vector<char> tmp; num.print(tmp); out << &tmp[0]; return out; } double to_double() const { if (size() == 0) return 0.0; double d = 0.0, base = ::pow(2.0, word_bits()); for (size_t i = size(); i --> 0;) d = d * base + (*this)[i]; return neg ? -d : d; } bool can_convert_to_int(int *result){ if (*this < Num(INT_MIN) || *this > Num(INT_MAX)) return false; unsigned temp = 0; if (word_bits() >= sizeof(temp)*CHAR_BIT){ if (words.size() > 0){ temp = (*this)[0]; } }else{ for (size_t i = words.size(); i --> 0;){ temp <<= word_bits(); temp += (*this)[i]; } } *result = neg ? -temp : temp; return true; } Num pow(size_t exponent) const { Num result(1), p(*this); for (; exponent; exponent >>= 1){ if (exponent & 1){ result = result * p; exponent--; } p = p*p; } return result; } Num mod_pow(Num exponent, const Num &modulus) const { Num result(1), base = (*this) % modulus; for (; exponent.size() > 0; exponent >>= 1){ if (exponent.get_bit(0)){ result = (result * base) % modulus; } base = (base * base) % modulus; } return result; } Num sqrt() const { Num n = *this; int bit = bitlength(); if (bit & 1) bit ^= 1; Num result = 0; for (; bit >= 0; bit -= 2){ Num tmp = result; tmp.set_bit(bit); if (n >= tmp){ n -= tmp; result.set_bit(bit + 1); } result >>= 1; } return result; } Num& operator ++(){ add_word(1); return *this; } Num& operator += (const Num &b){ return *this = add(*this, b); } Num& operator -= (const Num &b){ return *this = sub(*this, b); } Num& operator *= (const Num &b){ return *this = mul(*this, b); } Num& operator /= (const Num &b){ return *this = div(*this, b); } Num& operator %= (const Num &b){ return *this = mod(*this, b); } bool operator == (const Num &b) const { return cmp(*this, b) == 0; } bool operator != (const Num &b) const { return cmp(*this, b) != 0; } bool operator <= (const Num &b) const { return cmp(*this, b) <= 0; } bool operator >= (const Num &b) const { return cmp(*this, b) >= 0; } bool operator < (const Num &b) const { return cmp(*this, b) < 0; } bool operator > (const Num &b) const { return cmp(*this, b) > 0; } Num operator + (const Num &b) const { return add(*this, b); } Num operator - (const Num &b) const { return sub(*this, b); } Num operator * (const Num &b) const { return mul(*this, b); } Num operator / (const Num &b) const { return div(*this, b); } Num operator % (const Num &b) const { return mod(*this, b); } Num operator - ( ) const { return Num(*this).set_neg(!neg); } Num operator >> (size_t n_bits) const { return Num(*this) >>= n_bits; } Num operator << (size_t n_bits) const { return Num(*this) <<= n_bits; } }; int st[200]; typedef Num LL; vector<int> nast[200], skad[200]; int n; LL wyn=1; LL wyl[200], wym[200]; void dostepny(int x) { if (st[x]) return; st[x]=1; for (int i : nast[x]) dostepny(i); } LL nwd(LL a, LL b) { while (b!=0) { LL x=b; b=a%b; a=x; } return a; } LL nww(LL a, LL b) { return a/nwd(a, b)*b; } void oblicz(int x) { if (st[x]!=1 || nast[x].empty()) return; LL l=0, m=1; if (x==1) l=1; else { for (int i : skad[x]) { if (st[i]==0) continue; oblicz(i); LL ll=l*wym[i]+wyl[i]*m; LL mm=m*wym[i]; LL s=nwd(ll, mm); l=ll/s; m=mm/s; } } m*=nast[x].size(); st[x]=2; LL w=m/nwd(nast[x].size(), l); wyn=nww(wyn, w); LL s=nwd(l, m); wyl[x]=l/s; wym[x]=m/s; } int main() { ios_base::sync_with_stdio(false); cin>>n; for (int i=1; i<=n; ++i) { int r; cin>>r; for (int j=0; j<r; ++j) { int a; cin>>a; nast[i].push_back(a); skad[a].push_back(i); } } dostepny(1); for (int i=1; i<=n; ++i) oblicz(i); cout<<wyn<<endl; return 0; } |