#1012328 (C++23(gcc13)) No.2897 ２集合間距離

• 問題: No.2897 ２集合間距離
• ユーザー: pitP
• 提出日時: 2024-09-20 22:48:37
• 言語: C++23(gcc13) (gcc 13.2.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,701 ms / 3,500 ms
• コード長: 29,848 bytes
• コンパイル時間: 7,216 ms
• コンパイル使用メモリ: 361,236 KB
• 実行使用メモリ: 32,508 KB
• 最終ジャッジ日時: 2024-09-20 22:48:58
• 合計ジャッジ時間: 19,846 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	3 ms; 5,376 KB
testcase_13	AC	6 ms; 5,376 KB
testcase_14	AC	15 ms; 5,376 KB
testcase_15	AC	63 ms; 5,376 KB
testcase_16	AC	1,680 ms; 32,376 KB
testcase_17	AC	1,696 ms; 32,504 KB
testcase_18	AC	1,696 ms; 32,380 KB
testcase_19	AC	1,701 ms; 32,372 KB
testcase_20	AC	1,662 ms; 32,376 KB
testcase_21	AC	1,094 ms; 32,376 KB
testcase_22	AC	926 ms; 32,508 KB
testcase_23	AC	1,063 ms; 32,380 KB

ソースコード

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); }
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } 

typedef long long ll;
typedef vector<vector<int>> Graph;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define FOR(i,l,r) for (int i = l;i < (int)(r); i++)
#define rep(i,n) for (int i = 0;i < (int)(n); i++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define my_sort(x) sort(x.begin(), x.end())
#define my_max(x) *max_element(all(x))
#define my_min(x) *min_element(all(x))
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = (1<<30) - 1;
const ll LINF = (1LL<<62) - 1;
const int MOD = 998244353;
const int MOD2 = 1e9+7;
const double PI = acos(-1);
vector<int> di = {1,0,-1,0};
vector<int> dj = {0,1,0,-1};

#ifdef LOCAL
#  include <debug_print.hpp>
#  define debug_(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug_(...) (static_cast<void>(0))
#endif

// https://github.com/MitI-7/WaveletMatrix
enum {
    NOTFOUND = 0xFFFFFFFFFFFFFFFFLLU // 18446744073709551615 ~ 1.8x10^20
};

class SuccinctBitVector {
private:
    const uint64_t size;    // ビットベクトルのサイズ
    static const uint64_t blockBitNum = 16;
    static const uint64_t LEVEL_L = 512;
    static const uint64_t LEVEL_S = 16;

    std::vector<uint64_t> L;   // 大ブロック
    std::vector<uint16_t> S;   // 小ブロック
    std::vector<uint16_t> B;   // ビットベクトル

    uint64_t numOne = 0;       // 1bitの数

public:
    explicit SuccinctBitVector(const uint64_t n) : size(n) {
        const uint64_t s = (n + blockBitNum - 1) / blockBitNum + 1;   // ceil(n, blockSize)
        this->B.assign(s, 0);
        this->L.assign(n / LEVEL_L + 1, 0);
        this->S.assign(n / LEVEL_S + 1, 0);
    }

    // B[pos] = bit
    void setBit(const uint64_t bit, const uint64_t pos){
        assert(bit == 0 or bit == 1);
        assert(pos < this->size);

        const uint64_t blockPos = pos / blockBitNum;
        const uint64_t offset = pos % blockBitNum;
        if (bit == 1) { B.at(blockPos) |= (1LLU << offset); }
        else          { B.at(blockPos) &= (~(1LLU << offset)); }
    }

    // B[pos]
    uint64_t access(const uint64_t pos) {
        assert(pos < this->size);
        const uint64_t blockPos = pos / blockBitNum;
        const uint64_t offset   = pos % blockBitNum;
        return ((B.at(blockPos) >> offset) & 1);
    }

    void build() {
        uint64_t num = 0;
        for (uint64_t i = 0; i <= size; i++){
            if (i % LEVEL_L == 0) {
                L.at(i / LEVEL_L) = num;
            }
            if (i % LEVEL_S == 0) {
                S.at(i / LEVEL_S) = num - L.at(i / LEVEL_L);
            }
            if (i != size and i % blockBitNum == 0) {
                num += this->popCount(this->B.at(i / blockBitNum));
            }
        }
        this-> numOne = num;
    }

    // B[0, pos)のbitの数
    uint64_t rank(const uint64_t bit, const uint64_t pos) {
        assert(bit == 0 or bit == 1);
        assert(pos <= this->size);

        if (bit) {
            return L[pos / LEVEL_L] + S[pos / LEVEL_S] + popCount(B[pos / blockBitNum] & ((1 << (pos % blockBitNum)) - 1));
        }
        else {
            return pos - rank(1, pos);
        }
    }

    // rank番目のbitの位置 + 1(rankは1-origin)
    uint64_t select(const uint64_t bit, const uint64_t rank) {
        assert(bit == 0 or bit == 1);
        assert(rank > 0);
        if (bit == 0 and rank > this->size - this-> numOne) { return NOTFOUND; }
        if (bit == 1 and rank > this-> numOne)              { return NOTFOUND; }

        // 大ブロックL内を検索
        uint64_t large_idx = 0;
        {
            uint64_t left = 0;
            uint64_t right = L.size();
            while (right - left > 1) {
                uint64_t mid = (left + right) / 2;
                uint64_t r = L.at(mid);
                r = (bit) ? r : mid * LEVEL_L - L.at(mid);

                if (r < rank) {
                    left = mid;
                    large_idx = mid;
                } else {
                    right = mid;
                }
            }
        }

        // 小ブロックS内を検索
        uint64_t small_idx = (large_idx * LEVEL_L) / LEVEL_S;
        {
            uint64_t left = (large_idx * LEVEL_L) / LEVEL_S;
            uint64_t right = std::min(((large_idx  + 1) * LEVEL_L) / LEVEL_S, (uint64_t)S.size());
            while (right - left > 1) {
                uint64_t mid = (left + right) / 2;
                uint64_t r = L.at(large_idx) + S.at(mid);
                r = (bit) ? r :mid * LEVEL_S - r;

                if (r < rank) {
                    left = mid;
                    small_idx = mid;
                } else {
                    right = mid;
                }
            }
        }

        // Bをブロック単位で順番に探索
        uint64_t rank_pos = 0;
        {
            const uint64_t begin_block_idx = (small_idx * LEVEL_S) / blockBitNum;
            uint64_t total_bit = L.at(large_idx) + S.at(small_idx);
            if (bit == 0) {
                total_bit = small_idx * LEVEL_S - total_bit;
            }
            for (uint64_t i = 0;; ++i) {
                uint64_t b = popCount(B.at(begin_block_idx + i));
                if (bit == 0) {
                    b = blockBitNum - b;
                }
                if (total_bit + b >= rank) {
                    uint64_t block = (bit) ? B.at(begin_block_idx + i) : ~B.at(begin_block_idx + i);
                    rank_pos = (begin_block_idx + i) * blockBitNum + selectInBlock(block, rank - total_bit);
                    break;
                }
                total_bit += b;
            }
        }

        return rank_pos + 1;
    }

    uint64_t getNumOne() const {
        return numOne;
    }

    void debug() {
        std::cout << "LEVEL_L(" << L.size() << ")" << std::endl;
        for (uint64_t i = 0 ; i < L.size(); ++i) {
            std::cout << L.at(i) << ", ";
        }
        std::cout << std::endl;
        std::cout << "LEVEL_S(" << S.size() << ")" << std::endl;
        for (uint64_t i = 0 ; i < S.size(); ++i) {
            std::cout << S.at(i) << ", ";
        }
        std::cout << std::endl;
    }

private:
    uint64_t popCount(uint64_t x) {
        x = (x & 0x5555555555555555ULL) + ((x >> 1) & 0x5555555555555555ULL);
        x = (x & 0x3333333333333333ULL) + ((x >> 2) & 0x3333333333333333ULL);
        x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0fULL;
        x = x + (x >>  8);
        x = x + (x >> 16);
        x = x + (x >> 32);
        return x & 0x7FLLU;
    }

    uint64_t selectInBlock(uint64_t x, uint64_t rank) {
        uint64_t x1 = x - ((x & 0xAAAAAAAAAAAAAAAALLU) >> 1);
        uint64_t x2 = (x1 & 0x3333333333333333LLU) + ((x1 >> 2) & 0x3333333333333333LLU);
        uint64_t x3 = (x2 + (x2 >> 4)) & 0x0F0F0F0F0F0F0F0FLLU;

        uint64_t pos = 0;
        for (;;  pos += 8){
            uint64_t rank_next = (x3 >> pos) & 0xFFLLU;
            if (rank <= rank_next) break;
            rank -= rank_next;
        }

        uint64_t v2 = (x2 >> pos) & 0xFLLU;
        if (rank > v2) {
            rank -= v2;
            pos += 4;
        }

        uint64_t v1 = (x1 >> pos) & 0x3LLU;
        if (rank > v1){
            rank -= v1;
            pos += 2;
        }

        uint64_t v0  = (x >> pos) & 0x1LLU;
        if (v0 < rank){
            rank -= v0;
            pos += 1;
        }

        return pos;
    }
};

class WaveletMatrix {
private:
    std::vector<SuccinctBitVector> bit_arrays;
    std::vector<uint64_t> begin_one;                    // 各bitに着目したときの1の開始位置
    std::map<uint64_t, uint64_t> begin_alphabet;        // 最後のソートされた配列で各文字の開始位置
    std::vector<std::vector<uint64_t>> cumulative_sum;  // 各bitに着目したときの累積和

    uint64_t size;                                 // 与えられた配列のサイズ
    uint64_t maximum_element;                      // 文字数
    uint64_t bit_size;                             // 文字を表すのに必要なbit数

public:
    WaveletMatrix (const std::vector<uint64_t> &array) {
        assert(array.size() > 0);
        size = array.size();
        maximum_element =  *max_element(array.begin(), array.end()) + 1;
        bit_size = get_num_of_bit(maximum_element);
        if (bit_size == 0) {
            bit_size = 1;
        }

        for (uint64_t i = 0; i < bit_size; ++i) {
            SuccinctBitVector sv(size);
            bit_arrays.push_back(sv);
        }
        this->begin_one.resize(bit_size);
        this->cumulative_sum.resize(bit_size + 1, std::vector<uint64_t>(size + 1, 0));

        for (uint64_t j = 0; j < array.size(); ++j) {
            this->cumulative_sum.at(0).at(j + 1) = this->cumulative_sum.at(0).at(j) + array[j];
        }

        std::vector<uint64_t> v(array);
        for (uint64_t i = 0; i < bit_size; ++i) {

            std::vector<uint64_t> temp;
            // 0をtempにいれてく
            for (uint64_t j = 0; j < v.size(); ++j) {
                uint64_t c = v.at(j);
                uint64_t bit = (c >> (bit_size - i - 1)) & 1;  //　上からi番目のbit
                if (bit == 0) {
                    temp.push_back(c);
                    bit_arrays.at(i).setBit(0, j);
                }
            }

            this->begin_one.at(i) = temp.size();

            // 1をtempにいれてく
            for (uint64_t j = 0; j < v.size(); ++j) {
                uint64_t c = v.at(j);
                uint64_t bit = (c >> (bit_size - i - 1)) & 1;  //　上からi番目のbit
                if (bit == 1) {
                    temp.push_back(c);
                    bit_arrays.at(i).setBit(1, j);
                }
            }

            for (uint64_t j = 0; j < temp.size(); ++j) {
                this->cumulative_sum.at(i + 1).at(j + 1) = this->cumulative_sum.at(i + 1).at(j) + temp.at(j);
            }

            bit_arrays.at(i).build();
            v = temp;
        }

        // ソートされた配列内での各文字の位置を取得
        for (int i = v.size() - 1; i >= 0; --i) {
            this->begin_alphabet[v.at(i)] = i;
        }
    }

    // v[pos]
    uint64_t access(uint64_t pos) {
        if (pos >= this->size) { return NOTFOUND; }

        uint64_t c = 0;
        for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
            uint64_t bit = bit_arrays.at(i).access(pos);   // もとの数値のi番目のbit
            c = (c <<= 1) | bit;
            pos = bit_arrays.at(i).rank(bit, pos);
            if (bit) {
                pos += this->begin_one.at(i);
            }
        }
        return c;
    }

    // i番目のcの位置 + 1を返す。rankは1-origin
    uint64_t select(uint64_t c, uint64_t rank) {
        assert(rank > 0);
        if (c >= maximum_element) {
            return NOTFOUND;
        }
        if (this->begin_alphabet.find(c) == this->begin_alphabet.end()) {
            return NOTFOUND;
        }

        uint64_t index = this->begin_alphabet.at(c) + rank;
        for (uint64_t i = 0; i < bit_arrays.size(); ++i){
            uint64_t bit = ((c >> i) & 1);      // 下からi番目のbit
            if (bit == 1) {
                index -= this->begin_one.at(bit_size - i - 1);
            }
            index = this->bit_arrays.at(bit_size - i - 1).select(bit, index);
        }
        return index;
    }

    // v[begin_pos, end_pos)で最大値のindexを返す
    uint64_t maxRange(uint64_t begin_pos, uint64_t end_pos) {
        return quantileRange(begin_pos, end_pos, end_pos - begin_pos - 1);
    }

    // v[begin_pos, end_pos)で最小値のindexを返す
    uint64_t minRange(uint64_t begin_pos, uint64_t end_pos) {
        return quantileRange(begin_pos, end_pos, 0);
    }

    // v[begin_pos, end_pos)でk番目に小さい数値のindexを返す(kは0-origin)
    // つまり小さい順に並べてk番目の値
    uint64_t quantileRange(uint64_t begin_pos, uint64_t end_pos, uint64_t k) {
        if ((end_pos > size || begin_pos >= end_pos) || (k >= end_pos - begin_pos)) {
            return NOTFOUND;
        }

        uint64_t val = 0;
        for (uint64_t i = 0; i < bit_size; ++i) {
            const uint64_t num_of_zero_begin = bit_arrays.at(i).rank(0, begin_pos);
            const uint64_t num_of_zero_end = bit_arrays.at(i).rank(0, end_pos);
            const uint64_t num_of_zero = num_of_zero_end - num_of_zero_begin;     // beginからendまでにある0の数
            const uint64_t bit = (k < num_of_zero) ? 0 : 1;                       // k番目の値の上からi番目のbitが0か1か

            if (bit) {
                k -= num_of_zero;
                begin_pos = this->begin_one.at(i) + begin_pos - num_of_zero_begin;
                end_pos = this->begin_one.at(i) + end_pos - num_of_zero_end;
            }
            else {
                begin_pos = num_of_zero_begin;
                end_pos = num_of_zero_begin + num_of_zero;
            }

            val = ((val << 1) | bit);
        }

        uint64_t left = 0;
        for (uint64_t i = 0; i < bit_size; ++i) {
            const uint64_t bit = (val >> (bit_size - i - 1)) & 1;  // 上からi番目のbit
            left = bit_arrays.at(i).rank(bit, left);               // cのi番目のbitと同じ数値の数
            if (bit) {
                left += this->begin_one.at(i);
            }
        }

        const uint64_t rank = begin_pos + k - left + 1;
        return select(val, rank) - 1;
    }

    // v[0, pos)のcの数
    uint64_t rank(uint64_t c, uint64_t pos) {
        assert(pos < size);
        if (c >= maximum_element) {
            return 0;
        }
        if (this->begin_alphabet.find(c) == this->begin_alphabet.end()) {
            return 0;
        }

        for (uint64_t i = 0; i < bit_size; ++i) {
            uint64_t bit = (c >> (bit_size - i - 1)) & 1;  // 上からi番目のbit
            pos = bit_arrays.at(i).rank(bit, pos);         // cのi番目のbitと同じ数値の数
            if (bit) {
                pos += this->begin_one.at(i);
            }
        }

        uint64_t begin_pos = this->begin_alphabet.at(c);
        return pos - begin_pos;
    }

    // v[begin_pos, end_pos)で[min, max)に入る値の個数
    uint64_t rangeFreq(uint64_t begin_pos, uint64_t end_pos, uint64_t min_c, uint64_t max_c) {
        if ((end_pos > size || begin_pos >= end_pos) || (min_c >= max_c) || min_c >= maximum_element) {
            return 0;
        }

        const auto maxi_t = rankAll(max_c, begin_pos, end_pos);
        const auto mini_t = rankAll(min_c, begin_pos, end_pos);
        return std::get<1>(maxi_t) - std::get<1>(mini_t);
    }

    // v[0, pos)でcより小さい文字の数 <- 恐らくv[begin, end)
    uint64_t rankLessThan(uint64_t c, uint64_t begin, uint64_t end) {
        auto t = rankAll(c, begin, end);
        return std::get<1>(t);
    }

    // v[0, pos)でcより大きい文字の数 <- 恐らくv[begin, end)
    uint64_t rankMoreThan(uint64_t c, uint64_t begin, uint64_t end) {
        auto t = rankAll(c, begin, end);
        return std::get<2>(t);
    }

    // v[begin, end)で(cと同じ値の数、cより小さい値の数、cより大きい値の数)を求める
    std::tuple<uint64_t, uint64_t, uint64_t> rankAll(const uint64_t c, uint64_t begin, uint64_t end) {
        assert(end <= size);
        const uint64_t num = end - begin;

        if (begin >= end) {
            return std::make_tuple(0, 0, 0);
        }
        if (c >= maximum_element || end == 0) {
            return std::make_tuple(0, num, 0);
        }

        uint64_t rank_less_than = 0, rank_more_than = 0;
        for (size_t i = 0; i < bit_size && begin < end; ++i) {
            const uint64_t bit = (c >> (bit_size - i - 1)) & 1;

            const uint64_t rank0_begin = this->bit_arrays.at(i).rank(0, begin);
            const uint64_t rank0_end = this->bit_arrays.at(i).rank(0, end);
            const uint64_t rank1_begin = begin - rank0_begin;
            const uint64_t rank1_end = end - rank0_end;

            if (bit) {
                rank_less_than += (rank0_end - rank0_begin);    // i番目のbitが0のものは除外される
                begin = this->begin_one.at(i) + rank1_begin;
                end = this->begin_one.at(i) + rank1_end;
            } else {
                rank_more_than += (rank1_end - rank1_begin);    // i番目のbitが1のものは除外される
                begin = rank0_begin;
                end = rank0_end;
            }
        }

        const uint64_t rank = num - rank_less_than - rank_more_than;
        return std::make_tuple(rank, rank_less_than, rank_more_than);
    }

    // T[s, e)で出現回数が多い順にk個の(値，頻度)を返す
    // 頻度が同じ場合は値が小さいものが優先される
    std::vector<std::pair<uint64_t, uint64_t>> topk(uint64_t s, uint64_t e, uint64_t k) {
        assert(s < e);
        std::vector<std::pair<uint64_t, uint64_t>> result;

        // (頻度，深さ，値)の順でソート
        auto c = [](const std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &l, const std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &r) {
            // width
            if (std::get<0>(l) != std::get<0>(r)) {
                return std::get<0>(l) < std::get<0>(r);
            }
            // depth
            if (std::get<3>(l) != std::get<3>(r)) {
                return std::get<3>(l) > std::get<3>(r);
            }
            // value
            if (std::get<4>(l) != std::get<4>(r)) {
                return std::get<4>(l) > std::get<4>(r);
            }
            return true;
        };

        std::priority_queue<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>, std::vector<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>>, decltype(c)> que(c);  // width, left, right, depth, value
        que.push(std::make_tuple(e - s, s, e, 0, 0));

        while (not que.empty()) {
            auto element = que.top(); que.pop();
            uint64_t width, left, right, depth, value;
            std::tie(width, left, right, depth, value) = element;

            if (depth >= this->bit_size) {
                result.emplace_back(std::make_pair(value, right - left));
                if (result.size() >= k) {
                    break;
                }
                continue;
            }

            // 0
            const uint64_t left0 = this->bit_arrays.at(depth).rank(0, left);
            const uint64_t right0 = this->bit_arrays.at(depth).rank(0, right);
            if (left0 < right0) {
                que.push(std::make_tuple(right0 - left0, left0, right0, depth + 1, value));
            }

            // 1
            const uint64_t left1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, left);
            const uint64_t right1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, right);
            if (left1 < right1) {
                que.push(std::make_tuple(right1 - left1, left1, right1, depth + 1, value | (1 << (bit_size - depth - 1))));
            }
        }

        return result;
    };

    // T[begin_pos, end_pos)でx <= c < yを満たすcの和を返す
    uint64_t rangeSum(const uint64_t begin, const uint64_t end, const uint64_t x, const uint64_t y) {
        return rangeSum(begin, end, 0, 0, x, y);
    }

    // T[begin_pos, end_pos)でx <= c < yを満たす最大のcを返す
    uint64_t prevValue(const uint64_t begin_pos, const uint64_t end_pos, const uint64_t x, uint64_t y) {
        assert(end_pos <= size);
        const uint64_t num = end_pos - begin_pos;

        if (x >= y or y == 0) {
            return NOTFOUND;
        }
        if (y > maximum_element) {
            y = maximum_element;
        }

        if (begin_pos >= end_pos) {
            return NOTFOUND;
        }
        if (x >= maximum_element || end_pos == 0) {
            return NOTFOUND;
        }

        y--; // x <= c <= yにする

        std::stack<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, bool>> s;   // (begin, end, depth, c, tight)
        s.emplace(std::make_tuple(begin_pos, end_pos, 0, 0, true));

        while (not s.empty()) {
            uint64_t b, e, depth, c;
            bool tight;
            std::tie(b, e, depth, c, tight) = s.top(); s.pop();

            if (depth == bit_size) {
                if (c >= x) {
                    return c;
                }
                continue;
            }

            const uint64_t bit = (y >> (bit_size - depth - 1)) & 1;

            const uint64_t rank0_begin = this->bit_arrays.at(depth).rank(0, b);
            const uint64_t rank0_end = this->bit_arrays.at(depth).rank(0, e);
            const uint64_t rank1_begin = b - rank0_begin;
            const uint64_t rank1_end = e - rank0_end;

            // d番目のbitが0のものを使う
            const uint64_t b0 = rank0_begin;
            const uint64_t e0 = rank0_end;
            if (b0 != e0) { // 範囲がつぶれてない
                const uint64_t c0 = ((c << 1) | 0);
                s.emplace(std::make_tuple(b0, e0, depth + 1, c0, tight and bit == 0));
            }

            // d番目のbitが1のものを使う
            const uint64_t b1 = this->begin_one.at(depth) + rank1_begin;
            const uint64_t e1 = this->begin_one.at(depth) + rank1_end;
            if (b1 != e1) {
                if (not tight or bit == 1) {
                    const auto c1 = ((c << 1) | 1);
                    s.emplace(std::make_tuple(b1, e1, depth + 1, c1, tight));
                }
            }
        }

        return NOTFOUND;
    }

    // T[begin_pos, end_pos)でx <= c < yを満たす最小のcを返す
    uint64_t nextValue(const uint64_t begin_pos, const uint64_t end_pos, const uint64_t x, const uint64_t y) {
        assert(end_pos <= size);
        const uint64_t num = end_pos - begin_pos;

        if (x >= y or y == 0) {
            return NOTFOUND;
        }

        if (begin_pos >= end_pos) {
            return NOTFOUND;
        }
        if (x >= maximum_element || end_pos == 0) {
            return NOTFOUND;
        }

        std::stack<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, bool>> s;   // (begin, end, depth, c, tight)
        s.emplace(std::make_tuple(begin_pos, end_pos, 0, 0, true));

        while (not s.empty()) {
            uint64_t b, e, depth, c;
            bool tight;
            std::tie(b, e, depth, c, tight) = s.top(); s.pop();

            if (depth == bit_size) {
                if (c < y) {
                    return c;
                }
                continue;
            }

            const uint64_t bit = (x >> (bit_size - depth - 1)) & 1;

            const uint64_t rank0_begin = this->bit_arrays.at(depth).rank(0, b);
            const uint64_t rank0_end = this->bit_arrays.at(depth).rank(0, e);
            const uint64_t rank1_begin = b - rank0_begin;
            const uint64_t rank1_end = e - rank0_end;

            // d番目のbitが1のものを使う
            const uint64_t b1 = this->begin_one.at(depth) + rank1_begin;
            const uint64_t e1 = this->begin_one.at(depth) + rank1_end;
            if (b1 != e1) {
                const auto c1 = ((c << 1) | 1);
                s.emplace(std::make_tuple(b1, e1, depth + 1, c1, tight and bit == 1));
            }

            // d番目のbitが0のものを使う
            const uint64_t b0 = rank0_begin;
            const uint64_t e0 = rank0_end;
            if (b0 != e0) {
                if (not tight or bit == 0) {
                    const uint64_t c0 = ((c << 1) | 0);
                    s.emplace(std::make_tuple(b0, e0, depth + 1, c0, tight));
                }
            }
        }

        return NOTFOUND;
    }

    // T[s1, e1)とT[s2, e2)に共通して出現する要素を求める
    std::vector<std::tuple<uint64_t, uint64_t, uint64_t>> intersect(uint64_t _s1, uint64_t _e1, uint64_t _s2, uint64_t _e2) {
        assert(_s1 < _e1);
        assert(_s2 < _e2);

        std::vector<std::tuple<uint64_t, uint64_t, uint64_t>> intersection;

        std::queue<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>> que; // s1, e1, s2, e2, depth, value
        que.push(std::make_tuple(_s1, _e1, _s2, _e2, 0, 0));
        while (not que.empty()) {
            auto e = que.front(); que.pop();
            uint64_t s1, e1, s2, e2, depth, value;
            std::tie(s1, e1, s2, e2, depth, value) = e;

            if (depth >= this->bit_size) {
                intersection.emplace_back(std::make_tuple(value, e1 - s1, e2 - s2));
                continue;
            }

            // 0
            uint64_t s1_0 = this->bit_arrays.at(depth).rank(0, s1);
            uint64_t e1_0 = this->bit_arrays.at(depth).rank(0, e1);
            uint64_t s2_0 = this->bit_arrays.at(depth).rank(0, s2);
            uint64_t e2_0 = this->bit_arrays.at(depth).rank(0, e2);

            if (s1_0 != e1_0 and s2_0 != e2_0) {
                que.push(std::make_tuple(s1_0, e1_0, s2_0, e2_0, depth + 1, value));
            }

            // 1
            uint64_t s1_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, s1);
            uint64_t e1_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, e1);
            uint64_t s2_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, s2);
            uint64_t e2_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, e2);

            if (s1_1 != e1_1 and s2_1 != e2_1) {
                que.push(std::make_tuple(s1_1, e1_1, s2_1, e2_1, depth + 1, value | (1 << bit_size - depth - 1)));
            }
        }

        return intersection;
    };

private:
    uint64_t get_num_of_bit(uint64_t x) {
        if (x == 0) return 0;
        x--;
        uint64_t bit_num = 0;
        while (x >> bit_num) {
            ++bit_num;
        }
        return bit_num;
    }

    uint64_t rangeSum(const uint64_t begin, const uint64_t end, const uint64_t depth, const uint64_t c, const uint64_t x, const uint64_t y) {
        if (begin == end) {
            return 0;
        }

        if (depth == bit_size) {
            if (x <= c and c < y) {
                return c * (end - begin);   // 値 * 頻度
            }
            return 0;
        }

        const uint64_t next_c = ((uint64_t)1 << (bit_size - depth - 1)) | c;                   // 上からdepth番目のbitを立てる
        const uint64_t all_one_c = (((uint64_t)1 << (bit_size - depth - 1)) - 1) | next_c;     // depth以降のbitをたてる(これ以降全部1を選んだときの値)
        if(all_one_c < x or y <= c) {
            return 0;
        }

        // [begin, pos)のすべての要素は[x, y)
        if (x <= c and all_one_c < y) {
            return this->cumulative_sum.at(depth).at(end) - this->cumulative_sum.at(depth).at(begin);
        }

        const uint64_t rank0_begin = this->bit_arrays.at(depth).rank(0, begin);
        const uint64_t rank0_end = this->bit_arrays.at(depth).rank(0, end);
        const uint64_t rank1_begin = begin - rank0_begin;
        const uint64_t rank1_end = end - rank0_end;

        return rangeSum(rank0_begin, rank0_end, depth + 1, c, x, y) +
               rangeSum(this->begin_one.at(depth) + rank1_begin, this->begin_one[depth] + rank1_end, depth + 1, next_c, x, y);
    }
};
// vector<uint64_t> vec(N);
// WaveletMatrix wm(vec);
// wm.access(i)
// wm.select(val, rank)
// wm.maxRange(left, right)
// wm.minRange(left, right)
// wm.quantileRange(left, right, k)
// wm.rank(right)
// wm.rangeFreq(left, right, min_val, max_val)
// wm.rankLessThan(val, left, right)
// wm.rankMoreThan(val, left, right)
// wm.rankAll(val, left, right)
// wm.topk(left, right, k)
// wm.rangeSum(left, right, val_left, val_right)
// wm.prevValue(left, right, val_left, val_right)
// wm.nextValue(left, right, val_left, val_right)
// wm.intersect(left1, right1, left2, right2)

int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    int N; cin >> N;
    vector<int> x(N), y(N);
    vector<pii> C(N);
    rep(i, N){
        cin >> x[i] >> y[i];
        C[i] = make_pair(x[i] - y[i], x[i] + y[i]);
    }
    sort(all(C));
    rep(i, N){
        x[i] = C[i].first;
        y[i] = C[i].second;
    }
    debug_(x, y);
    vector<uint64_t> d(N);
    rep(i, N) d[i] = y[i];
    WaveletMatrix wm(d);

    auto is_ok = [&](int L, int z, int w){
        auto l = lower_bound(all(x), z - L) - x.begin();
        auto r = upper_bound(all(x), z + L) - x.begin();
        int cnt = wm.rangeFreq(l, r, max(w - L, 0), w + L + 1);
        debug_(cnt, l, r, L);
        return cnt > 0;
    };

    int ans = INF;
    int M; cin >> M;
    rep(_, M){
        int z, w; cin >> z >> w;
        int Z = z - w, W = z + w;
        int ok = 10000, ng = -1;
        while(abs(ok - ng) > 1){
            int mid = (ok + ng) >> 1;
            (is_ok(mid, Z, W) ? ok : ng) = mid;
        }
        chmin(ans, ok);
    }
    cout << ans << endl;
}