#include <bits/stdc++.h>
using namespace std;
const long long MOD=1000000007;
// const long long MOD=998244353;
#define LOCAL
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(),(x).end()
const int INF=1e9;
const long long IINF=1e18;
const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
const char dir[4]={'D','R','U','L'};

template<typename T>
istream &operator>>(istream &is,vector<T> &v){
    for (T &x:v) is >> x;
    return is;
}
template<typename T>
ostream &operator<<(ostream &os,const vector<T> &v){
    for (int i=0;i<v.size();++i){
        os << v[i] << (i+1==v.size()?"": " ");
    }
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const pair<T,U> &p){
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template<typename T,typename U,typename V>
ostream&operator<<(ostream &os,const tuple<T,U,V> &t){
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
    return os;
}
template<typename T,typename U,typename V,typename W>
ostream&operator<<(ostream &os,const tuple<T,U,V,W> &t){
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const map<T,U> &m){
    os << '{';
    for (auto itr=m.begin();itr!=m.end();){
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr!=m.end()) os << ',';
    }
    os << '}';
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const unordered_map<T,U> &m){
    os << '{';
    for (auto itr=m.begin();itr!=m.end();){
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr!=m.end()) os << ',';
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const set<T> &s){
    os << '{';
    for (auto itr=s.begin();itr!=s.end();){
        os << *itr;
        if (++itr!=s.end()) os << ',';
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const multiset<T> &s){
    os << '{';
    for (auto itr=s.begin();itr!=s.end();){
        os << *itr;
        if (++itr!=s.end()) os << ',';
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const unordered_set<T> &s){
    os << '{';
    for (auto itr=s.begin();itr!=s.end();){
        os << *itr;
        if (++itr!=s.end()) os << ',';
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const deque<T> &v){
    for (int i=0;i<v.size();++i){
        os << v[i] << (i+1==v.size()?"": " ");
    }
    return os;
}

void debug_out(){cerr << '\n';}
template<class Head,class... Tail>
void debug_out(Head&& head,Tail&&... tail){
    cerr << head;
    if (sizeof...(Tail)>0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) cerr << " ";\
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n';\
cerr << " ";\
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template<typename T> T gcd(T x,T y){return y!=0?gcd(y,x%y):x;}
template<typename T> T lcm(T x,T y){return x/gcd(x,y)*y;}

template<class T1,class T2> inline bool chmin(T1 &a,T2 b){
    if (a>b){a=b; return true;} return false;
}
template<class T1,class T2> inline bool chmax(T1 &a,T2 b){
    if (a<b){a=b; return true;} return false;
}
#pragma endregion

struct Mo{
    int sz;
    vector<int> left,right;
    Mo(int n):sz((int)sqrt(n)){}
    void insert(int l,int r){
        left.emplace_back(l);
        right.emplace_back(r);
    }
    template<typename ADDL,typename ADDR,typename DELL,typename DELR,typename REM>
    void build(const ADDL &add_left,const ADDR &add_right,const DELL &del_left,const DELR &del_right,const REM &rem){
        int q=left.size();
        vector<int> ord(q);
        iota(ord.begin(),ord.end(),0);
        sort(ord.begin(),ord.end(),[&](int a,int b){
            return (left[a]/sz!=left[b]/sz?left[a]<left[b]:right[a]<right[b]);
        });
        int l=0,r=0;
        for (int idx:ord){
            while(l>left[idx]) add_left(--l);
            while(r<right[idx]) add_right(r++);
            while(l<left[idx]) del_left(l++);
            while(r>right[idx]) del_right(--r);
            rem(idx);
        }
    }
    template<typename ADD,typename DEL,typename REM>
    void build(const ADD &add,const DEL &del,const REM &rem){
        build(add,add,del,del,rem);
    }
};

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N; cin >> N;
    vector<int> X(N); cin >> X;

    Mo mo(N);
    int Q; cin >> Q;
    vector<int> x(Q);
    for (int i=0;i<Q;++i){
        int l,r; cin >> l >> r >> x[i];
        mo.insert(--l,r);
    }

    vector<int> ans(Q,INF);
    multiset<int> s;
    auto add=[&](int idx){s.emplace(X[idx]);};
    auto del=[&](int idx){s.erase(s.find(X[idx]));};
    auto rem=[&](int idx){
        auto itr=s.lower_bound(x[idx]);
        if (itr!=s.end()) chmin(ans[idx],*itr-x[idx]);
        if (itr!=s.begin()) chmin(ans[idx],x[idx]-*(--itr));
    };
    mo.build(add,add,del,del,rem);

    for (int a:ans) cout << a << '\n';
}