# Xor-Set

You are given two sets of integers: $A$ and $B$. You need to output the sum of elements in the set $C = \{x | x = a \oplus b, a \in A, b \in B\}$ modulo $998244353$, where $\oplus$ denotes the bitwise XOR operation. Each number should be counted only once.

For example, if $A = \{2, 3\}$ and $B = \{2, 3\}$ you should count integer $1$ only once, despite the fact that you can get it as $3 \oplus 2$ and as $2 \oplus 3$. So the answer for this case is equal to $1 + 0 = 1$.

Let’s call a segment $[l; r]$ a set of integers $\{l, l+1, \dots, r\}$.

The set $A$ is given as a union of $n_A$ segments, the set $B$ is given as a union of $n_B$ segments.Input

The first line contains a single integer $n_A$ ($1 \le n_A \le 100$).

The $i$-th of the next $n_A$ lines contains two integers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le 10^{18}$), describing a segment of values of set $A$.

The next line contains a single integer $n_B$ ($1 \le n_B \le 100$).

The $i$-th of the next $n_B$ lines contains two integers $l_j$ and $r_j$ ($1 \le l_j \le r_j \le 10^{18}$), describing a segment of values of set $B$.

Note that segments in both sets may intersect.Output

Print one integer — the sum of all elements in set $C = \{x | x = a \oplus b, a \in A, b \in B\}$ modulo $998244353$.Examplesinput

2
3 5
5 8
3
1 2
1 9
2 9


output

112


input

1
1 9
2
2 4
2 10


output

120


Note

In the second example, we can discover that the set $C = \{0,1,\dots,15\}$, which means that all numbers between $0$ and $15$ can be represented as $a \oplus b$.

Solution:

#undef _GLIBCXX_DEBUG

#include <bits/stdc++.h>

using namespace std;

template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
return '"' + s + '"';
}

string to_string(const char* s) {
}

string to_string(bool b) {
return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
bool first = true;
string res = "{";
for (int i = 0; i < static_cast<int>(v.size()); i++) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(v[i]);
}
res += "}";
return res;
}

template <size_t N>
string to_string(bitset<N> v) {
string res = "";
for (size_t i = 0; i < N; i++) {
res += static_cast<char>('0' + v[i]);
}
return res;
}

template <typename A>
string to_string(A v) {
bool first = true;
string res = "{";
for (const auto &x : v) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(x);
}
res += "}";
return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

void debug_out(Head H, Tail... T) {
cerr << " " << to_string(H);
debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}

template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;

constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}

template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
else v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}

const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }

Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }

template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}

Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

template <typename U>
friend const Modular<U>& abs(const Modular<U>& v) { return v; }

template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

template <typename U>
friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

private:
Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}

template <typename T>
bool IsZero(const Modular<T>& number) {
return number() == 0;
}

template <typename T>
string to_string(const Modular<T>& number) {
}

template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
return stream << number();
}

template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, int64_t>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}

/*
using ModType = int;

struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

int main() {
ios::sync_with_stdio(false);
cin.tie(0);
const int BITS = 61;
vector<vector<vector<long long>>> all(2, vector<vector<long long>>(BITS));
vector<vector<vector<long long>>> any(2, vector<vector<long long>>(BITS));
for (int rot = 0; rot < 2; rot++) {
auto Add = [&](long long from, long long to) {
int bits = (from == to ? 0 : 64 - __builtin_clzll(from ^ to));
assert(to - from + 1 == (1LL << bits));
all[rot][bits].push_back(from);
};
int n;
cin >> n;
for (int i = 0; i < n; i++) {
long long L, R;
cin >> L >> R;
while ((L | (L - 1)) <= R) {
long long new_L = (L | (L - 1)) + 1;
L = new_L;
}
while (L <= (R & (R + 1))) {
long long new_R = (R & (R + 1)) - 1;
R = new_R;
}
assert(L == R + 1);
}
for (int k = 0; k < BITS; k++) {
sort(all[rot][k].begin(), all[rot][k].end());
all[rot][k].resize(unique(all[rot][k].begin(), all[rot][k].end()) - all[rot][k].begin());
sort(any[rot][k].begin(), any[rot][k].end());
any[rot][k].resize(unique(any[rot][k].begin(), any[rot][k].end()) - any[rot][k].begin());
if (k < BITS - 1) {
for (long long x : all[rot][k]) {
any[rot][k + 1].push_back(x & (~(1LL << k)));
}
for (long long x : any[rot][k]) {
any[rot][k + 1].push_back(x & (~(1LL << k)));
}
}
}
}
vector<pair<int, int>> trie(1, make_pair(-1, -1));
vector<bool> finish(1, false);
Mint ans = 0;
for (int k = BITS - 1; k >= 0; k--) {
vector<long long> v;
auto Do = [&](long long x, long long y) {
long long z = x ^ y;
v.push_back(z);
};
for (long long x : all[0][k]) {
for (long long y : all[1][k]) {
Do(x, y);
}
}
for (long long x : all[0][k]) {
for (long long y : any[1][k]) {
Do(x, y);
}
}
for (long long x : any[0][k]) {
for (long long y : all[1][k]) {
Do(x, y);
}
}
sort(v.begin(), v.end());
v.resize(unique(v.begin(), v.end()) - v.begin());
for (long long x : v) {
int t = 0;
bool good = true;
for (int b = BITS - 1; b >= k; b--) {
int& to = ((x & (1LL << b)) ? trie[t].first : trie[t].second);
if (to == -1) {
to = (int) trie.size();
trie.emplace_back(-1, -1);
finish.push_back(false);
}
t = ((x & (1LL << b)) ? trie[t].first : trie[t].second);
if (finish[t]) {
good = false;
break;
}
}
if (good) {
finish[t] = true;
ans += (Mint(x) + Mint(x + (1LL << k) - 1)) * Mint(1LL << k) / Mint(2);
}
}
}
cout << ans << '\n';
return 0;
}