Problem: Lord Tirek is a centaur and the main antagonist in the season four finale episodes in the series "My Little Pony: Friendship Is Magic". In "Twilight's Kingdom" (Part 1), Tirek escapes from Tartarus and drains magic from ponies to grow stronger.

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The core skill of Tirek is called Absorb Mana. It takes all mana from a magic creature and gives them to the caster.

Now to simplify the problem, assume you have n ponies (numbered from 1 to n). Each pony has three attributes:

  * si : amount of mana that the pony has at time 0; 
  * mi : maximum mana that the pony can have; 
  * ri : mana regeneration per unit time. 



Lord Tirek will do m instructions, each of them can be described with three integers: ti, li, ri. The instruction means that at time ti, Tirek will use Absorb Mana on ponies with numbers from li to ri (both borders inclusive). We'll give you all the m instructions in order, count how much mana Tirek absorbs for each instruction.

Input

The first line contains an integer n (1 ≤ n ≤ 105) — the number of ponies. Each of the next n lines contains three integers si, mi, ri (0 ≤ si ≤ mi ≤ 105; 0 ≤ ri ≤ 105), describing a pony. 

The next line contains an integer m (1 ≤ m ≤ 105) — the number of instructions. Each of the next m lines contains three integers ti, li, ri (0 ≤ ti ≤ 109; 1 ≤ li ≤ ri ≤ n), describing an instruction of Lord Tirek. The instructions are given in strictly increasing order of ti (all ti are distinct).

Output

For each instruction, output a single line which contains a single integer, the total mana absorbed in this instruction.

Examples

Input

5
0 10 1
0 12 1
0 20 1
0 12 1
0 10 1
2
5 1 5
19 1 5


Output

25
58

Note

Every pony starts with zero mana. For the first instruction, each pony has 5 mana, so you get 25 mana in total and each pony has 0 mana after the first instruction.

For the second instruction, pony 3 has 14 mana and other ponies have mana equal to their mi.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
struct pony {
  long long s, m, r, t;
} ponys[100005];
bool cmp(pony &x, pony &y) { return x.t < y.t; }
struct node {
  long long l, r, latest;
  long long *sm, *sr, *t;
} nodes[100005 << 3];
void build(long long ord, long long l, long long r) {
  nodes[ord].latest = 0;
  nodes[ord].l = l, nodes[ord].r = r;
  if (l == r) {
    nodes[ord].sm = &ponys[l].m;
    nodes[ord].sr = &ponys[l].r;
    nodes[ord].t = &ponys[l].t;
    return;
  }
  int m = (l + r) >> 1;
  build(ord << 1, l, m);
  build(ord << 1 | 1, m + 1, r);
  pony *tmp = new pony[r - l + 1];
  for (int i = 0; i < r - l + 1; i++) tmp[i] = ponys[l + i];
  sort(tmp, tmp + r - l + 1, cmp);
  nodes[ord].sm = new long long[r - l + 2];
  nodes[ord].sr = new long long[r - l + 2];
  nodes[ord].t = new long long[r - l + 2];
  nodes[ord].sm[0] = nodes[ord].sr[0] = nodes[ord].t[0] = 0;
  for (int i = 1; i < r - l + 2; i++) {
    nodes[ord].sm[i] = tmp[i - 1].m + nodes[ord].sm[i - 1];
    nodes[ord].sr[i] = tmp[i - 1].r + nodes[ord].sr[i - 1];
    nodes[ord].t[i] = tmp[i - 1].t;
  }
  delete[] tmp;
}
long long mana_obserbed(long long ord, long long t, long long l, long long r) {
  long long res = 0;
  if (nodes[ord].latest > 0)
    nodes[ord << 1].latest = nodes[ord << 1 | 1].latest = nodes[ord].latest;
  if (nodes[ord].l == l && nodes[ord].r == r) {
    if (nodes[ord].latest > 0) {
      if (l == r)
        res = min(ponys[l].m, ponys[l].r * (t - nodes[ord].latest));
      else {
        int len = nodes[ord].r - nodes[ord].l + 2;
        int tmp = upper_bound(nodes[ord].t + 1, nodes[ord].t + len,
                              t - nodes[ord].latest) -
                  nodes[ord].t;
        res = nodes[ord].sm[tmp - 1] +
              (nodes[ord].sr[len - 1] - nodes[ord].sr[tmp - 1]) *
                  (t - nodes[ord].latest);
      }
      nodes[ord].latest = t;
      return res;
    } else if (nodes[ord].latest == 0 && l == r) {
      res = min(ponys[l].m, ponys[l].s + ponys[l].r * t);
      nodes[ord].latest = t;
      return res;
    }
  }
  int m = (nodes[ord].l + nodes[ord].r) >> 1;
  if (r <= m)
    res += mana_obserbed(ord << 1, t, l, r);
  else if (m < l)
    res += mana_obserbed(ord << 1 | 1, t, l, r);
  else
    res += mana_obserbed(ord << 1, t, l, m) +
           mana_obserbed(ord << 1 | 1, t, m + 1, r);
  nodes[ord].latest = nodes[ord << 1].latest == nodes[ord << 1 | 1].latest
                          ? nodes[ord << 1].latest
                          : -1;
  return res;
}
int main() {
  long long n, m, t, l, r;
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    cin >> ponys[i].s >> ponys[i].m >> ponys[i].r;
    if (ponys[i].r)
      ponys[i].t = (ponys[i].m + ponys[i].r - 1) / ponys[i].r;
    else
      ponys[i].t = 0x7fffffffffffffff;
  }
  build(1, 1, n);
  cin >> m;
  for (long long i = 1; i <= m; i++) {
    cin >> t >> l >> r;
    cout << mana_obserbed(1, t, l, r) << endl;
  }
  return 0;
}