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>
#define ll long long int
#define mp make_pair
#define pb push_back
#define ff first 
#define ss second
#define mod 1000000007
#define lim 100005
#define mx 20005
#define nfs_mw ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;

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

int main()
{
	ll ans = 0;
	int i,j,n,w,s,v,maxmw = 0;
	cin>>n;
	vector<box> all;
	for(i=0; i<n; i++){
		cin>>w>>s>>v;
		all.pb({w,s,v});
	}
	sort(all.begin(), all.end());
	ll dp[mx] = {};ll dp2[mx] = {};
	dp[0] = 0;
	for(i=0; i<n; i++){
		for(j=1; ((all[i].s + all[i].w) >= j); j++){
			dp2[j] = max({dp2[j-1], ((all[i].w<=j)?(dp[j-all[i].w] + all[i].v):0), dp[j]});
		}
		swap(dp,dp2);
	}
	cout<<dp[all[n-1].s+all[n-1].w];
}