Problem:
Score : 1200 points

Problem Statement

Snuke loves flags.

Snuke is placing N flags on a line.

The i-th flag can be placed at either coordinate x_i or coordinate y_i.

Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.

Constraints

2 ≤ N ≤ 10^{4}

1 ≤ x_i, y_i ≤ 10^{9}

x_i and y_i are integers.

Input

The input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the answer.

Sample Input 1

3
1 3
2 5
1 9

Sample Output 1

4

The optimal solution is to place the first flag at coordinate 1, the second flag at coordinate 5 and the third flag at coordinate 9. The smallest distance between two of the flags is 4 in this case.

Sample Input 2

5
2 2
2 2
2 2
2 2
2 2

Sample Output 2

0

There can be more than one flag at the same position.

Sample Input 3

22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269

Sample Output 3

17

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

#define rep(i, m, n) for(int(i) = (int)(m); i < (int)(n); ++i)
#define rep2(i, m, n) for(int(i) = (int)(n)-1; i >= (int)(m); --i)
#define REP(i, n) rep(i, 0, n)
#define REP2(i, n) rep2(i, 0, n)
#define all(hoge) (hoge).begin(), (hoge).end()
#define en '\n'
using ll = long long;
using ull = unsigned long long;
template <class T>
using vec = vector<T>;
template <class T>
using vvec = vector<vec<T>>;
typedef pair<ll, ll> P;
using tp = tuple<ll, ll, ll>;
constexpr long long INF = 1LL << 60;
constexpr int INF_INT = 1 << 25;
//constexpr long long MOD = (ll)1e9 + 7;
constexpr long long MOD = 998244353LL;
using ld = long double;
static const ld pi = 3.141592653589793L;
typedef vector<ll> Array;
typedef vector<Array> Matrix;

template <class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

//グラフ関連
struct Edge {
    ll to, cap, rev;
    Edge(ll _to, ll _cap, ll _rev) {
        to = _to;
        cap = _cap;
        rev = _rev;
    }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &G, ll from, ll to, ll cap, bool revFlag, ll revCap) {
    G[from].push_back(Edge(to, cap, (ll)G[to].size()));
    if(revFlag)
        G[to].push_back(Edge(from, revCap, (ll)G[from].size() - 1));
}

template <class E>
struct csr {
    std::vector<int> start;
    std::vector<E> elist;
    csr(int n, const std::vector<std::pair<int, E>> &edges)
        : start(n + 1), elist(edges.size()) {
        for(auto e : edges) {
            start[e.first + 1]++;
        }
        for(int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        auto counter = start;
        for(auto e : edges) {
            elist[counter[e.first]++] = e.second;
        }
    }
};

// Reference:
// R. Tarjan,
// Depth-First Search and Linear Graph Algorithms
struct scc_graph {
  public:
    scc_graph(int n) : _n(n) {}

    int num_vertices() { return _n; }

    void add_edge(int from, int to) { edges.push_back({from, {to}}); }

    // @return pair of (# of scc, scc id)
    std::pair<int, std::vector<int>> scc_ids() {
        auto g = csr<edge>(_n, edges);
        int now_ord = 0, group_num = 0;
        std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
        visited.reserve(_n);
        auto dfs = [&](auto self, int v) -> void {
            low[v] = ord[v] = now_ord++;
            visited.push_back(v);
            for(int i = g.start[v]; i < g.start[v + 1]; i++) {
                auto to = g.elist[i].to;
                if(ord[to] == -1) {
                    self(self, to);
                    low[v] = std::min(low[v], low[to]);
                } else {
                    low[v] = std::min(low[v], ord[to]);
                }
            }
            if(low[v] == ord[v]) {
                while(true) {
                    int u = visited.back();
                    visited.pop_back();
                    ord[u] = _n;
                    ids[u] = group_num;
                    if(u == v)
                        break;
                }
                group_num++;
            }
        };
        for(int i = 0; i < _n; i++) {
            if(ord[i] == -1)
                dfs(dfs, i);
        }
        for(auto &x : ids) {
            x = group_num - 1 - x;
        }
        return {group_num, ids};
    }

    std::vector<std::vector<int>> scc() {
        auto ids = scc_ids();
        int group_num = ids.first;
        std::vector<int> counts(group_num);
        for(auto x : ids.second)
            counts[x]++;
        std::vector<std::vector<int>> groups(ids.first);
        for(int i = 0; i < group_num; i++) {
            groups[i].reserve(counts[i]);
        }
        for(int i = 0; i < _n; i++) {
            groups[ids.second[i]].push_back(i);
        }
        return groups;
    }

  private:
    int _n;
    struct edge {
        int to;
    };
    std::vector<std::pair<int, edge>> edges;
};

struct two_sat {
  public:
    two_sat() : _n(0), scc(0) {}
    two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}

    void add_clause(int i, bool f, int j, bool g) {
        assert(0 <= i && i < _n);
        assert(0 <= j && j < _n);
        scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
        scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
    }
    bool satisfiable() {
        auto id = scc.scc_ids().second;
        for(int i = 0; i < _n; i++) {
            if(id[2 * i] == id[2 * i + 1])
                return false;
            _answer[i] = id[2 * i] < id[2 * i + 1];
        }
        return true;
    }
    std::vector<bool> answer() { return _answer; }

  private:
    int _n;
    std::vector<bool> _answer;
    scc_graph scc;
};

void solve() {
    ll n;
    cin >> n;
    vvec<ll> x(n, vec<ll>(2));
    REP(i, n) {
        cin >> x[i][0] >> x[i][1];
    }

    auto check = [&](ll d) -> bool {
        two_sat ts(n);
        REP(i, n) {
            rep(j, i + 1, n) {
                REP(k, 2) {
                    REP(w, 2) {
                        if(abs(x[i][k] - x[j][w]) < d) {
                            ts.add_clause(i, k, j, w);
                        }
                    }
                }
            }
        }
        return ts.satisfiable();
    };

    ll l = 0;
    ll r = 1e9 + 1;
    while(l + 1 < r) {
        ll m = l + r >> 1;
        if(check(m))
            l = m;
        else
            r = m;
    }
    cout << l << en;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    /*
    ll t;
    cin >> t;
    while(t--)*/
    solve();

    return 0;
}