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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
void debug() {cout<<endl;}
template<typename T,typename... Args>
void debug(T x,Args... args) {cout<<x<<" ";debug(args...);}
#define forn(i,a,b) for(int i=a;i<b;++i)
#define pb push_back
#define F first
#define S second
#define endl "\n"
typedef long long ll;
typedef pair<int, int> pii;

const int N = 1005, M = 10005;
ll dp[N][M], inf = 1e18;
int n;

struct block{
  int w, s, v;
  bool operator < (const block &b)const{
    return w+s > b.w+b.s;
  }
};

vector<block> blocks;


ll f(int i, int j){
  if(j < 0)return -inf;
  if(i == n)return 0;
  ll &ans = dp[i][j];
  if(ans != -1)return ans;
  ans = 0;
  ans = max(ans, f(i+1, min(j-blocks[i].w, blocks[i].s))+blocks[i].v);
  ans = max(ans, f(i+1, j));
  return ans;
}




int main() {
  ios::sync_with_stdio(0); cin.tie(0);

  int w, s, v;
  cin >> n;
  forn(i, 0, n){
    cin >> w >> s >> v;
    blocks.pb({w, s, v});
  }
  sort(blocks.begin(), blocks.end());
  memset(dp, -1, sizeof dp);
  ll mx = 0;
  forn(i, 0, n){
    mx = max(mx, f(i+1, blocks[i].s)+blocks[i].v);
  }
  cout << mx << endl;

}