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)

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

struct block{int w,s;long long v;};
bool cmp(block a,block b){
  return a.w+a.s<b.w+b.s;
}
long long ans,dp[20001];//dp[i]:重さiでの最大価値
/*
重ねる時は相手のwも含めてのsなのでu.s-v.w>v.s-u.w 足して小さい方から積む？
*/
template<typename T>
void chmax(T &a,T b){
  if(a<b)a=b;
}

int main(){
  int n;cin>>n;
  vector<block> a(n);
  for(int i=0;i<n;i++){
    int w,s,v;cin>>w>>s>>v;
    a[i]={w,s,v};
  }
  sort(a.begin(),a.end(),cmp);
  for(int i=0;i<n;i++)
    for(int j=a[i].s;j>=0;j--)chmax(dp[j+a[i].w],dp[j]+a[i].v);
  for(int i=0;i<20001;i++)chmax(ans,dp[i]);
  cout<<ans<<endl;
}