#include<bits/stdc++.h>
#define REP(i,n) for(int i=0,i##_len=int(n);i<i##_len;++i)
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
#define All(x) (x).begin(),(x).end()
#define rAll(x) (x).rbegin(),(x).rend()
using namespace std;
using ll = long long;

template<typename T> class SegmentTree{
  private:
    typedef std::function<T(T,T)> F;
    int n;
    T d0;
    vector<T> vertex;
    F f;
    F g;
  public:
    SegmentTree(F f,F g,T d):d0(d),f(f),g(g){}
    void init(int _n){
        n=1;
        while(n<_n) n*=2;
        vertex.resize(2*n-1,d0);
    }
    void build(const vector<T> &v){
        int n_=v.size();
        init(n_);
        for(int i=0;i<n_;i++) vertex[n+i-1]=v[i];
        for(int i=n-2;i>=0;i--)
        vertex[i]=f(vertex[2*i+1],vertex[2*i+2]);
    }
    void update(int i,T x){
        int k=i+n-1;
        vertex[k]=g(vertex[k],x);
        while(k>0){
            k=(k-1)/2;
            vertex[k]=f(vertex[2*k+1],vertex[2*k+2]);
        }
        return;
    }
    T query(int l,int r){
        T vl=d0,vr=d0;
        l+=n-1;
        r+=n-1;
        for(;l<=r;l/=2,r=r/2-1){
            if(l%2==0) vl=f(vl,vertex[l]);
            if(r&1) vr=f(vr,vertex[r]);
        }
        return f(vl,vr);
    }
};

int main(){
    int N;cin>>N;
    assert(1<=N&&N<=100000);
    using T = tuple<ll,ll,ll,ll>;
    vector<T> X(N);
    vector<int> A;
    const int MAX=1e9;
    REP(i,N) {
        int a,b,c;
        cin>>a>>b>>c;
        assert(1<=a&&a<=MAX);
        assert(1<=b&&b<=MAX);
        assert(1<=c&&c<=MAX);
        X[i]=tie(a,b,c,i);
        A.push_back(a);
    }
    sort(All(A));
    sort(All(X));
    const ll inf = 1LL<<50;
    SegmentTree<ll> dp([](ll a,ll b){return max(a,b);},[](ll a,ll b){return b;},0);
    SegmentTree<bool> bl([](bool a,bool b){return a|b;},[](bool a,bool b){return b;},false);
    dp.init(N);
    bl.init(N);
    priority_queue<pair<int,int>> que;
    REP(i,N){
        ll a,b,c,t;
        tie(a,b,c,t)=X[i];
        while(!que.empty()&&que.top().first<a){
            int ind=que.top().second;que.pop();
            ll pl=get<1>(X[ind]);
            pl+=dp.query(0,i-1);
            if(bl.query(ind,N-1)) pl=inf;
            dp.update(ind,pl);
            bl.update(i-1,true);
        }
        if(b-c>=a){
            que.push(make_pair(b-c,i));
            continue;
        }
        int k=upper_bound(All(A),b-c)-A.begin();
        ll pl=b;
        if(k>0) pl+=dp.query(0,k-1);
        dp.update(i,pl);
        if(k>0) bl.update(k-1,true);
    }
    while(!que.empty()){
        int ind=que.top().second;que.pop();
        ll pl=get<1>(X[ind]);
        pl+=dp.query(0,N-1);
        if(bl.query(ind,N-1)) pl=inf;
        dp.update(ind,pl);
        bl.update(N-1,true);
    }
    REP(i,N){
        int k=upper_bound(All(A),get<1>(X[i])-get<2>(X[i]))-A.begin();
        if(k>0) dp.update(i,max(dp.query(i,i),dp.query(0,k-1)));
    }
    vector<ll> ans(N);
    REP(i,N) ans[get<3>(X[i])]=dp.query(i,i);
    REP(i,N){
        if(ans[i]>=inf) cout<<"BAN"<<endl;
        else cout<<ans[i]<<endl;
    }
}