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 pb push_back
#define mp make_pair
#define inside sl<=l&&r<=sr
#define outside r<sl||sr<l
#define INF 1000000009
#define mod 1000000007
using namespace std;
typedef long long ll;
int n;
struct block{
	ll w, s, v;
};
block arr[1003];

int com(const block& a, const block& b){
	return a.w+a.s < b.w+b.s;
}

ll dp[1003][20004];

int main(){
	//freopen("stl.gir", "r", stdin);
	
	cin >> n;
	for (int i = 0; i < n; i++){
		cin >> arr[i].w >> arr[i].s >> arr[i].v;
	}
	
	sort(arr, arr+n, com);
	
	/*for (int i = 0; i < n; i++){
		cout << "(" << arr[i].w << ", " << arr[i].s << ", " << arr[i].v << ")\n";
	}*/
	
	// dp[i][j] = ilk i blok kullanılarak toplam ağırlığı j olan max value
	// dp[i][j] = max(dp[i-1][j], dp[i-1][j-w[i]]+v[i]);
	
	for (int i = 0; i < n; i++){
		for (int j = 0; j < 20004; j++){
			if (i == 0){
				if (j < arr[i].w) dp[i][j] = 0;
				else dp[i][j] = arr[i].v;
			} else if (j == 0){
				dp[i][j] = 0;
			} else {
				dp[i][j] = max(dp[i-1][j], dp[i][j-1]);
				if (j-arr[i].w >= 0 && arr[i].s >= j-arr[i].w) dp[i][j] = max(dp[i][j], dp[i-1][j-arr[i].w]+arr[i].v);
			}
		}
	}
	
	//cout << dp[1][0] << endl;
	cout << dp[n-1][20003] << endl;
	
}