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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

typedef long long int ll;

const int N = 1111;
const int M = 1e4+7;

struct tower
{
  int w, s;
  ll v;
  tower(){}
  tower(int w, int s, ll v)
  : w(w), s(s), v(v){}
  bool operator<(const tower& t)const
  {
    return w + s > t.w + t.s;
  }
};

tower T[N];
ll dp[N][M];

ll f(int i, int w)
{
  if(w >= M) return -1e15;
  if(~dp[i][w]) return dp[i][w];
  ll& ans = dp[i][w];
  
  if(i == 0) return dp[i][w] = T[i].s >= w ? T[i].v : -1e15;
  
  ans = -1e15;
  
  if(T[i].s >= w) ans = f(i-1, T[i].w + w) + T[i].v;
  ans = max(ans, f(i-1, w));
  
  return ans;
}

int main()
{
  ios_base::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  
  int n;
  cin >> n;
  
  for(int i=0;i<n;++i)
    cin >> T[i].w >> T[i].s >> T[i].v;
  
  sort(T, T + n);
  
  memset(dp, -1 , sizeof dp);
  
  cout << f(n-1, 0) << endl;
  
  return 0;
}