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<iostream>
#include<cstdio>
#include<algorithm>
#include<cassert>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
#include <cstring>
using namespace std;
#define MOD 1000000007
#define MOD2 998244353
#define INF ((1<<30)-1)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P; 
const int N = 1000006;
//////////////////////////////

struct Block {
	Int w, s, v;
	bool operator < (const Block &a)const {
		return w + s < a.w + a.s;
	}
} Blocks[1003];

int n;
Int dp[1003][22000];

int main() { 
	ios_base::sync_with_stdio(0); cin.tie(0);//fflush(stdout);
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> Blocks[i].w >> Blocks[i].s >> Blocks[i].v;
	}

	sort(Blocks, Blocks + n);
	
	for (int i = 1; i <= n; i++) {
		int ind = i - 1;
		for (int j = 0; j < 22000; j++) {
			dp[i][j] = dp[i - 1][j];
			if (j - Blocks[ind].w >= 0 && j - Blocks[ind].w <= Blocks[ind].s) {
				dp[i][j] = max(dp[i][j], dp[i - 1][j - Blocks[i].w] + Blocks[i].v);
			}
		}
	}
	
	Int ans = 0;
	for (int j = 0; j < 22000; j++) {
		ans = max(ans, dp[n][j]);
	}
	cout << ans << endl;

	return 0;
}