#include <bits/stdc++.h> typedef long long int lli; using namespace std; #define MAX3 1010 #define MAX4 10010 #define MAX5 100010 #define MAX6 1000010 template <typename T > void dbg(T last) { cout << last << "\n"; } template <typename T, typename ...args> void dbg(T current, args ...next) { cout << current << ' '; dbg(next...); } // BigInt from https://codeforces.com/contest/98/submission/143267789 constexpr int digits(int base) noexcept {return base <= 1 ? 0 : 1 + digits(base / 10);}constexpr int BASE = 1000'000'000;constexpr int BASE_DIGITS = digits(BASE); struct BigInt {vector<int> a;int sign;BigInt():sign(1) {}BigInt(long long v) {*this = v;}BigInt& operator=(long long v) {sign = 1;if (v < 0) {sign = -1;v = -v;}a.clear();for (; v > 0; v = v / BASE)a.push_back((int)(v % BASE));return *this;} BigInt(const string &s){read(s);}void read(const string& s) {sign = 1;a.clear();int pos = 0;while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {if (s[pos] == '-') sign = -sign;++pos;}for (int i = (int)s.size() - 1; i >= pos; i -= BASE_DIGITS) {int x = 0;for (int j = max(pos, i - BASE_DIGITS + 1); j <= i; j++)x = x * 10 + s[j] - '0';a.push_back(x);} trim();}friend istream& operator>>(istream &stream, BigInt &v) {string s;stream >> s;v.read(s);return stream;}friend ostream& operator<<(ostream &stream, const BigInt &v) {if (v.sign == -1 && !v.isZero())stream << '-'; stream << (v.a.empty() ? 0 : v.a.back());for (int i = (int) v.a.size() - 2; i >= 0; --i)stream << setw(BASE_DIGITS) << setfill('0') << v.a[i]; return stream;}bool operator<(const BigInt &v) const {if (sign != v.sign)return sign < v.sign;if (a.size() != v.a.size()) return a.size() * sign < v.a.size() * v.sign;for (int i = ((int) a.size()) - 1; i >= 0; i--)if (a[i] != v.a[i])return a[i] * sign < v.a[i] * sign;return false; }bool operator>(const BigInt &v) const {return v < *this;}bool operator<=(const BigInt &v) const {return !(v < *this);}bool operator>=(const BigInt &v) const {return !(*this < v);} bool operator==(const BigInt &v) const {return sign == v.sign && a == v.a;} bool operator!=(const BigInt &v) const {return !(*this == v);} BigInt operator-() const {BigInt res = *this;if (isZero())return res;res.sign = -sign;return res;}friend int __compare_abs(const BigInt& x, const BigInt& y) {if (x.a.size() != y.a.size()) {return x.a.size() < y.a.size() ? -1 : 1;} for (int i = ((int) x.a.size()) - 1; i >= 0; --i) {if (x.a[i] != y.a[i]) {return x.a[i] < y.a[i] ? -1 : 1;}}return 0;}void __internal_add(const BigInt& v) {if (a.size() < v.a.size()) {a.resize(v.a.size(), 0);}for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) { if (i == (int) a.size()) a.push_back(0);a[i] += carry + (i < (int) v.a.size() ? v.a[i] : 0);carry = a[i] >= BASE; if (carry) a[i] -= BASE;}}void __internal_sub(const BigInt& v) {for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0); carry = a[i] < 0;if (carry) a[i] += BASE;}this->trim();}BigInt& operator+=(const BigInt& v) {if (sign == v.sign) {__internal_add(v); } else {if (__compare_abs(*this, v) >= 0) {__internal_sub(v);} else {BigInt vv = v;swap(*this, vv);__internal_sub(vv);}} return *this;}BigInt& operator-=(const BigInt& v) {if (sign == v.sign) {if (__compare_abs(*this, v) >= 0) {__internal_sub(v);} else {BigInt vv = v;swap(*this, vv); __internal_sub(vv);this->sign = -this->sign;}} else {__internal_add(v);}return *this;}template< typename L, typename R >typename std::enable_if<std::is_convertible<L, BigInt>::value &&std::is_convertible<R, BigInt>::value,BigInt>::type friend operator-(L&& l, R&& r) {BigInt result(std::forward<L>(l));result -= r;return result;}friend pair<BigInt, BigInt> divmod(const BigInt &a1, const BigInt &b1) {assert(b1 > 0); long long norm = BASE / (b1.a.back() + 1);BigInt x = a1.abs() * norm;BigInt y = b1.abs() * norm;BigInt q = 0, r = 0;q.a.resize(x.a.size()); for (int i = (int)x.a.size() - 1; i >= 0; i--) {r *= BASE;r += x.a[i];long long s1 = r.a.size() <= y.a.size() ? 0 : r.a[y.a.size()];long long s2 = r.a.size() <= (int)y.a.size() - 1 ? 0 : r.a[(int)y.a.size() - 1];long long d = (long long)(((long long) BASE * s1 + s2) / y.a.back());r -= y * d;while (r < 0) {r += y, --d;}q.a[i] = d;}q.sign = a1.sign * b1.sign;r.sign = a1.sign; q.trim();r.trim();auto res = make_pair(q, r / norm);if (res.second < 0) res.second += b1;return res;}BigInt operator/(const BigInt &v) const {if (v < 0) return divmod(-*this, -v).first;return divmod(*this, v).first;}BigInt& operator/=(const BigInt &v) {*this = *this / v;return *this;} BigInt operator%(const BigInt &v) const {return divmod(*this, v).second;}BigInt& operator%=(const BigInt &v) {*this = *this % v;return *this;} BigInt mul_simple(const BigInt &v) const {BigInt res;res.sign = sign * v.sign;res.a.resize(a.size() + v.a.size()); for (int i = 0; i < (int) a.size(); ++i)if (a[i])for (int j = 0, carry = 0; j < (int) v.a.size() || carry; ++j) {long long cur = res.a[i + j] + (long long) a[i] * (j < (int) v.a.size() ? v.a[j] : 0) + carry;carry = (int) (cur / BASE);res.a[i + j] = (int) (cur % BASE);}res.trim();return res;}BigInt operator*(const BigInt &v) const {return mul_simple(v);}BigInt& operator*=(const BigInt &v) {*this = *this * v; return *this;}BigInt& operator/=(int v) {assert(v > 0);if (llabs(v) >= BASE) {*this /= BigInt(v);return *this;}if (v < 0) sign = -sign, v = -v;for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {long long cur = a[i] + rem * (long long) BASE;a[i] = (int) (cur / v);rem = (int) (cur % v);}trim(); return *this;}BigInt operator/(int v) const {assert(v > 0);if (llabs(v) >= BASE) {return *this / BigInt(v);}BigInt res = *this;res /= v;return res;}BigInt& operator*=(int v) {if (llabs(v) >= BASE) { *this *= BigInt(v);return *this;}if (v < 0)sign = -sign, v = -v;for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {if (i == (int) a.size())a.push_back(0);long long cur = a[i] * (long long) v + carry;carry = (int) (cur / BASE);a[i] = (int) (cur % BASE);}trim();return *this;}BigInt operator*(int v) const {if (llabs(v) >= BASE) {return *this * BigInt(v);}BigInt res = *this;res *= v;return res;}long long operator%(long long v) const { assert(v < BASE);if (v < 0)v = -v;long long m = 0;for (int i = (int)a.size() - 1; i >= 0; --i)m = (int)((a[i] + m * (long long) BASE) % v); return m * sign;}BigInt& operator%=(long long v) {assert(v < BASE);*this = *this % v;return *this;}friend BigInt __gcd(const BigInt &a, const BigInt &b) {BigInt A=a,B=b,ans=1;for (;!(A.a[0]&1)&&!(B.a[0]&1);A/=2,B/=2,ans*=2);for (;;){if (A.a.size()==0&&A.a[0]==0) return B*ans;if (B.a.size()==0&&B.a[0]==0) return A*ans;for (;!(A.a[0]&1);A/=2);for (;!(B.a[0]&1);B/=2);A>B?A-=B:B-=A;}}void trim() {while (!a.empty() && a.back()==0)a.pop_back();if (a.empty())sign = 1;}bool isZero() const {return a.empty() || (a.size()==1 && a[0]==0);}BigInt abs() const {if(sign == -1)return -*this;return *this;}template< typename L, typename R >typename std::enable_if<std::is_convertible<L, BigInt>::value &&std::is_convertible<R, BigInt>::value &&std::is_lvalue_reference<R&&>::value,BigInt>::type friend operator+(L&& l, R&& r) {BigInt result(std::forward<L>(l)); result += r;return result;}template< typename L, typename R >typename std::enable_if<std::is_convertible<L, BigInt>::value &&std::is_convertible<R, BigInt>::value &&std::is_rvalue_reference<R&&>::value,BigInt>::type friend operator+(L&& l, R&& r) {BigInt result(std::move(r));result += l;return result;}}; //-----------------------------------------------------------------------------------------------// vector<int> tab[MAX3]; int cnt[MAX3]; BigInt numerator[MAX3]; BigInt denominator[MAX3]; BigInt answerator[MAX3]; int n; BigInt zero("0"); BigInt one("1"); void add(int i, int j, BigInt x) { BigInt a = numerator[i]; BigInt b = denominator[i]; BigInt c = numerator[j]; BigInt d = denominator[j]; d*=x; if (b == zero) { numerator[i] = c; denominator[i] = d; // dbg(i, c,"/",d); return; } BigInt a1 = a; a1*=d; BigInt b1 = b; b1*=c; BigInt n = a1; n+=b1; BigInt nd = b; nd *= d; BigInt g =__gcd(n,nd); n /= g; nd /= g; numerator[i] = n; denominator[i] = nd; // dbg(a,"/",b, " + ", c,"/",d, " = ", n,"/",nd); // dbg(i, c,"/",d); } void work() { numerator[1] = 1; denominator[1] = 1; for (int i=1;i<=n;i++) { if (denominator[i] != zero && tab[i].size() !=0) { int xx = tab[i].size(); BigInt x(xx); BigInt an = denominator[i]; an*=x; BigInt gg =__gcd(an,numerator[i]); answerator[i] = an; answerator[i] /= gg; for (int j=0;j<tab[i].size();j++) { add(tab[i][j], i, x); } } } BigInt ans("1"); // for (int i=1;i<=n;i++) // { // if (denominator[i] != zero) // { // ans = (ans*denominator[i])/(__gcd(ans, denominator[i])); // // dbg(numerator[i], denominator[i]); // } // } for (int i=1;i<=n;i++) { if (answerator[i] != zero) { BigInt gg =__gcd(ans, answerator[i]); ans *=answerator[i]; ans /=gg; // dbg(denominator[i]); } } cout << ans << "\n"; } void solve() { cin >> n; for (int i=1;i<=n;i++) { int x,a; cin >> x; for (int j=0;j<x;j++) { cin >> a; tab[i].push_back(a); } } work(); } int main() { std::ios::sync_with_stdio(false); solve(); return 0; } /* 7 3 2 3 5 2 3 6 3 5 6 7 1 6 1 7 0 0 7 3 2 3 5 2 3 6 3 5 6 7 1 6 1 7 0 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 | #include <bits/stdc++.h> typedef long long int lli; using namespace std; #define MAX3 1010 #define MAX4 10010 #define MAX5 100010 #define MAX6 1000010 template <typename T > void dbg(T last) { cout << last << "\n"; } template <typename T, typename ...args> void dbg(T current, args ...next) { cout << current << ' '; dbg(next...); } // BigInt from https://codeforces.com/contest/98/submission/143267789 constexpr int digits(int base) noexcept {return base <= 1 ? 0 : 1 + digits(base / 10);}constexpr int BASE = 1000'000'000;constexpr int BASE_DIGITS = digits(BASE); struct BigInt {vector<int> a;int sign;BigInt():sign(1) {}BigInt(long long v) {*this = v;}BigInt& operator=(long long v) {sign = 1;if (v < 0) {sign = -1;v = -v;}a.clear();for (; v > 0; v = v / BASE)a.push_back((int)(v % BASE));return *this;} BigInt(const string &s){read(s);}void read(const string& s) {sign = 1;a.clear();int pos = 0;while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {if (s[pos] == '-') sign = -sign;++pos;}for (int i = (int)s.size() - 1; i >= pos; i -= BASE_DIGITS) {int x = 0;for (int j = max(pos, i - BASE_DIGITS + 1); j <= i; j++)x = x * 10 + s[j] - '0';a.push_back(x);} trim();}friend istream& operator>>(istream &stream, BigInt &v) {string s;stream >> s;v.read(s);return stream;}friend ostream& operator<<(ostream &stream, const BigInt &v) {if (v.sign == -1 && !v.isZero())stream << '-'; stream << (v.a.empty() ? 0 : v.a.back());for (int i = (int) v.a.size() - 2; i >= 0; --i)stream << setw(BASE_DIGITS) << setfill('0') << v.a[i]; return stream;}bool operator<(const BigInt &v) const {if (sign != v.sign)return sign < v.sign;if (a.size() != v.a.size()) return a.size() * sign < v.a.size() * v.sign;for (int i = ((int) a.size()) - 1; i >= 0; i--)if (a[i] != v.a[i])return a[i] * sign < v.a[i] * sign;return false; }bool operator>(const BigInt &v) const {return v < *this;}bool operator<=(const BigInt &v) const {return !(v < *this);}bool operator>=(const BigInt &v) const {return !(*this < v);} bool operator==(const BigInt &v) const {return sign == v.sign && a == v.a;} bool operator!=(const BigInt &v) const {return !(*this == v);} BigInt operator-() const {BigInt res = *this;if (isZero())return res;res.sign = -sign;return res;}friend int __compare_abs(const BigInt& x, const BigInt& y) {if (x.a.size() != y.a.size()) {return x.a.size() < y.a.size() ? -1 : 1;} for (int i = ((int) x.a.size()) - 1; i >= 0; --i) {if (x.a[i] != y.a[i]) {return x.a[i] < y.a[i] ? -1 : 1;}}return 0;}void __internal_add(const BigInt& v) {if (a.size() < v.a.size()) {a.resize(v.a.size(), 0);}for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) { if (i == (int) a.size()) a.push_back(0);a[i] += carry + (i < (int) v.a.size() ? v.a[i] : 0);carry = a[i] >= BASE; if (carry) a[i] -= BASE;}}void __internal_sub(const BigInt& v) {for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0); carry = a[i] < 0;if (carry) a[i] += BASE;}this->trim();}BigInt& operator+=(const BigInt& v) {if (sign == v.sign) {__internal_add(v); } else {if (__compare_abs(*this, v) >= 0) {__internal_sub(v);} else {BigInt vv = v;swap(*this, vv);__internal_sub(vv);}} return *this;}BigInt& operator-=(const BigInt& v) {if (sign == v.sign) {if (__compare_abs(*this, v) >= 0) {__internal_sub(v);} else {BigInt vv = v;swap(*this, vv); __internal_sub(vv);this->sign = -this->sign;}} else {__internal_add(v);}return *this;}template< typename L, typename R >typename std::enable_if<std::is_convertible<L, BigInt>::value &&std::is_convertible<R, BigInt>::value,BigInt>::type friend operator-(L&& l, R&& r) {BigInt result(std::forward<L>(l));result -= r;return result;}friend pair<BigInt, BigInt> divmod(const BigInt &a1, const BigInt &b1) {assert(b1 > 0); long long norm = BASE / (b1.a.back() + 1);BigInt x = a1.abs() * norm;BigInt y = b1.abs() * norm;BigInt q = 0, r = 0;q.a.resize(x.a.size()); for (int i = (int)x.a.size() - 1; i >= 0; i--) {r *= BASE;r += x.a[i];long long s1 = r.a.size() <= y.a.size() ? 0 : r.a[y.a.size()];long long s2 = r.a.size() <= (int)y.a.size() - 1 ? 0 : r.a[(int)y.a.size() - 1];long long d = (long long)(((long long) BASE * s1 + s2) / y.a.back());r -= y * d;while (r < 0) {r += y, --d;}q.a[i] = d;}q.sign = a1.sign * b1.sign;r.sign = a1.sign; q.trim();r.trim();auto res = make_pair(q, r / norm);if (res.second < 0) res.second += b1;return res;}BigInt operator/(const BigInt &v) const {if (v < 0) return divmod(-*this, -v).first;return divmod(*this, v).first;}BigInt& operator/=(const BigInt &v) {*this = *this / v;return *this;} BigInt operator%(const BigInt &v) const {return divmod(*this, v).second;}BigInt& operator%=(const BigInt &v) {*this = *this % v;return *this;} BigInt mul_simple(const BigInt &v) const {BigInt res;res.sign = sign * v.sign;res.a.resize(a.size() + v.a.size()); for (int i = 0; i < (int) a.size(); ++i)if (a[i])for (int j = 0, carry = 0; j < (int) v.a.size() || carry; ++j) {long long cur = res.a[i + j] + (long long) a[i] * (j < (int) v.a.size() ? v.a[j] : 0) + carry;carry = (int) (cur / BASE);res.a[i + j] = (int) (cur % BASE);}res.trim();return res;}BigInt operator*(const BigInt &v) const {return mul_simple(v);}BigInt& operator*=(const BigInt &v) {*this = *this * v; return *this;}BigInt& operator/=(int v) {assert(v > 0);if (llabs(v) >= BASE) {*this /= BigInt(v);return *this;}if (v < 0) sign = -sign, v = -v;for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {long long cur = a[i] + rem * (long long) BASE;a[i] = (int) (cur / v);rem = (int) (cur % v);}trim(); return *this;}BigInt operator/(int v) const {assert(v > 0);if (llabs(v) >= BASE) {return *this / BigInt(v);}BigInt res = *this;res /= v;return res;}BigInt& operator*=(int v) {if (llabs(v) >= BASE) { *this *= BigInt(v);return *this;}if (v < 0)sign = -sign, v = -v;for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {if (i == (int) a.size())a.push_back(0);long long cur = a[i] * (long long) v + carry;carry = (int) (cur / BASE);a[i] = (int) (cur % BASE);}trim();return *this;}BigInt operator*(int v) const {if (llabs(v) >= BASE) {return *this * BigInt(v);}BigInt res = *this;res *= v;return res;}long long operator%(long long v) const { assert(v < BASE);if (v < 0)v = -v;long long m = 0;for (int i = (int)a.size() - 1; i >= 0; --i)m = (int)((a[i] + m * (long long) BASE) % v); return m * sign;}BigInt& operator%=(long long v) {assert(v < BASE);*this = *this % v;return *this;}friend BigInt __gcd(const BigInt &a, const BigInt &b) {BigInt A=a,B=b,ans=1;for (;!(A.a[0]&1)&&!(B.a[0]&1);A/=2,B/=2,ans*=2);for (;;){if (A.a.size()==0&&A.a[0]==0) return B*ans;if (B.a.size()==0&&B.a[0]==0) return A*ans;for (;!(A.a[0]&1);A/=2);for (;!(B.a[0]&1);B/=2);A>B?A-=B:B-=A;}}void trim() {while (!a.empty() && a.back()==0)a.pop_back();if (a.empty())sign = 1;}bool isZero() const {return a.empty() || (a.size()==1 && a[0]==0);}BigInt abs() const {if(sign == -1)return -*this;return *this;}template< typename L, typename R >typename std::enable_if<std::is_convertible<L, BigInt>::value &&std::is_convertible<R, BigInt>::value &&std::is_lvalue_reference<R&&>::value,BigInt>::type friend operator+(L&& l, R&& r) {BigInt result(std::forward<L>(l)); result += r;return result;}template< typename L, typename R >typename std::enable_if<std::is_convertible<L, BigInt>::value &&std::is_convertible<R, BigInt>::value &&std::is_rvalue_reference<R&&>::value,BigInt>::type friend operator+(L&& l, R&& r) {BigInt result(std::move(r));result += l;return result;}}; //-----------------------------------------------------------------------------------------------// vector<int> tab[MAX3]; int cnt[MAX3]; BigInt numerator[MAX3]; BigInt denominator[MAX3]; BigInt answerator[MAX3]; int n; BigInt zero("0"); BigInt one("1"); void add(int i, int j, BigInt x) { BigInt a = numerator[i]; BigInt b = denominator[i]; BigInt c = numerator[j]; BigInt d = denominator[j]; d*=x; if (b == zero) { numerator[i] = c; denominator[i] = d; // dbg(i, c,"/",d); return; } BigInt a1 = a; a1*=d; BigInt b1 = b; b1*=c; BigInt n = a1; n+=b1; BigInt nd = b; nd *= d; BigInt g =__gcd(n,nd); n /= g; nd /= g; numerator[i] = n; denominator[i] = nd; // dbg(a,"/",b, " + ", c,"/",d, " = ", n,"/",nd); // dbg(i, c,"/",d); } void work() { numerator[1] = 1; denominator[1] = 1; for (int i=1;i<=n;i++) { if (denominator[i] != zero && tab[i].size() !=0) { int xx = tab[i].size(); BigInt x(xx); BigInt an = denominator[i]; an*=x; BigInt gg =__gcd(an,numerator[i]); answerator[i] = an; answerator[i] /= gg; for (int j=0;j<tab[i].size();j++) { add(tab[i][j], i, x); } } } BigInt ans("1"); // for (int i=1;i<=n;i++) // { // if (denominator[i] != zero) // { // ans = (ans*denominator[i])/(__gcd(ans, denominator[i])); // // dbg(numerator[i], denominator[i]); // } // } for (int i=1;i<=n;i++) { if (answerator[i] != zero) { BigInt gg =__gcd(ans, answerator[i]); ans *=answerator[i]; ans /=gg; // dbg(denominator[i]); } } cout << ans << "\n"; } void solve() { cin >> n; for (int i=1;i<=n;i++) { int x,a; cin >> x; for (int j=0;j<x;j++) { cin >> a; tab[i].push_back(a); } } work(); } int main() { std::ios::sync_with_stdio(false); solve(); return 0; } /* 7 3 2 3 5 2 3 6 3 5 6 7 1 6 1 7 0 0 7 3 2 3 5 2 3 6 3 5 6 7 1 6 1 7 0 0 */ |