Problem:
Score : 100 points

Problem Statement

There are N blocks, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Block i has a weight of w_i, a solidness of s_i and a value of v_i.

Taro has decided to build a tower by choosing some of the N blocks and stacking them vertically in some order.
Here, the tower must satisfy the following condition:

For each Block i contained in the tower, the sum of the weights of the blocks stacked above it is not greater than s_i.

Find the maximum possible sum of the values of the blocks contained in the tower.

Constraints

All values in input are integers.

1 \leq N \leq 10^3

1 \leq w_i, s_i \leq 10^4

1 \leq v_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
w_1 s_1 v_1
w_2 s_2 v_2
:
w_N s_N v_N

Output

Print the maximum possible sum of the values of the blocks contained in the tower.

Sample Input 1

3
2 2 20
2 1 30
3 1 40

Sample Output 1

50

If Blocks 2, 1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.

Sample Input 2

4
1 2 10
3 1 10
2 4 10
1 6 10

Sample Output 2

40

Blocks 1, 2, 3, 4 should be stacked in this order from top to bottom.

Sample Input 3

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

8
9 5 7
6 2 7
5 7 3
7 8 8
1 9 6
3 3 3
4 1 7
4 5 5

Sample Output 4

22

We should, for example, stack Blocks 5, 6, 8, 4 in this order from top to bottom.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#define NDEBUG
NDEBUG


#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cstring>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <set>
#include <sstream>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <memory>
#include <queue>
#include <random>


using namespace std;

template<class T>
using vec = std::vector<T>;


template<class T>
vec<T> makeVec(const int n1, const T initValue) {
  return vec<T>(n1, initValue);
}


#define FOR(i, n) for (int i = 0; i < (n); ++i)


#define all(c) c.begin(), c.end()


// TC_REMOVE_BEGIN
/// caide keep
bool __hack = std::ios::sync_with_stdio(false);
/// caide keep
auto __hack1 = cin.tie(nullptr);
// TC_REMOVE_END


// Section with adoption of array and vector algorithms.


//#include <ext/pb_ds/tree_policy.hpp>
//#include <ext/pb_ds/assoc_container.hpp>
//
//template <class T> using StdTree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;


namespace template_util {
    

    constexpr int bytecount(uint64_t x) {
        return x ? 1 + bytecount(x >> 8) : 0;
    }

    template<int N>
    struct bytetype {
        
    };

    
    /// caide keep
    template<uint64_t N>
    struct minimal_uint : bytetype<bytecount(N)> {
    };
}


template<class T>
T next(istream& in) {
    T ret;
    in >> ret;
    return ret;
}


#define dbg(...) ;


void solve(istream& in, ostream& out) {
  auto n = next<int>(in);
  vec<int> ws(n), ss(n);
  vec<int64_t> vs(n);
  vec<int> ids(n);
  FOR(i, n) {
    ids[i] = i;
  }
  int maxS = 0;
  FOR(i, n) {
    ws[i] = next<int>(in);
    ss[i] = next<int>(in);
    vs[i] = next<int64_t>(in);
    maxS = max(maxS, ss[i]);
  }

  sort(all(ids), [&] (int i1, int i2) -> bool {
    return ss[i1] + ws[i1] < ss[i2] + ws[i2];
  });

  vec<int64_t> f(maxS + 1, -1);
  vec<int64_t> nxt(maxS + 1, -1);
  f[0] = 0;

  dbg(ids);

  int64_t res = 0;
  FOR(i, n) {
    FOR(j, maxS + 1) {
      if (f[j] != -1) {
        nxt[j] = max(nxt[j], f[j]);
        if (j <= ss[ids[i]] && j + ws[ids[i]] <= maxS) {
          nxt[j + ws[ids[i]]] = max(nxt[j + ws[ids[i]]], f[j] + vs[ids[i]]);
        }
        if (j <= ss[ids[i]]) {
          res = max(res, f[j] + vs[ids[i]]);
        }
      }
    }
    f = nxt;
    nxt = makeVec<int64_t>(maxS + 1, -1);
  }
  out << res << "\n";
}

//#include <fstream>


int main() {
//  ifstream fin("bridges.in");
//  ofstream fout("bridges.out");
    solve(cin, cout);
//  solve(fin, fout);
    return 0;
}