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: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

const int mxs = 1e3 + 1;
using ll = long long;

int n;
vector<ll> w, s, v;
unordered_map<int, string> dp;

ll solve(ll mslack, string mask){
    if(stoi(mask) == 0 || mslack == 0) return 0;
    ll res = -1;
    for(int i = 0; i < n; i++){
        if((mask[i] - '0') && w[i] <= mslack){
            string tmp = mask;
            tmp[i] = '0';
            res = max(res, v[i] + solve(min(mslack - w[i], s[i]), tmp));
        }
    }
    return res;
}

int main(){
    cin>>n;
    w.resize(n); s.resize(n); v.resize(n);
    for(int i = 0; i < n; i++){
        cin>>w[i]>>s[i]>>v[i];
    }
    string mask(n, '1');
    // int mask = (1 << n) - 1;
    ll res = solve((ll)1e5, mask);
    cout<<res<<endl;
    return 0;
}