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 (Clang 3.8.0) (judge verdict: Accepted)

#include <cmath>
#include <iostream>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <bitset>
#include <algorithm>
#include <functional>
#include <utility>
#include <iomanip>

#define int long long int
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )

using namespace std;

typedef pair<int, int> P;

const int INF = 1e15;
const int MOD = 1e9+7;

struct block{
    int w, s, v;
};

bool compare(block a, block b){
    return a.w + a.s < b.w + b.s;
}

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;
    vector<block> vb(n);
    rep(i, n){
        int w, s, v;
        cin >> w >> s >> v;
        vb[i] = {w, s, v};
    }
    sort(ALL(vb), compare);

    vector<vector<int>> dp(n + 1, vector<int>(20001));
    rep(i, n){
        rep(j, 20000){
            dp[i+1][j] = max(dp[i+1][j], dp[i][j]);
            if(j > vb[i].s){
                continue;
            }
            if(j + vb[i].w > 20000){
                continue;
            }
            dp[i+1][j+vb[i].w] = max(dp[i+1][j+vb[i].w], dp[i][j] + vb[i].v);
        }
    }

    int ans = 0;
    rep(i, 20001){
        ans = max(ans, dp[n][i]);
    }
    cout << ans << endl;

    return 0;
}