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 <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define rrep(i,n) for(int i=((int)(n)-1);i>=0;(i)--)
#define rrep1(i,n) for(int i=((int)(n));i>0;(i)--)
#define sz(c) ((int)(c).size())
#define all(x) (x).begin(),(x).end()
#define mp make_pair
#define pb push_back
#define fi first
#define se second

using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef pair<int, int> P;
typedef pair<int, pair<int, int> > PP;
const int MAX=1e3+10;


int N;
vi w,s;
vll v;
int S, W;

void input(){
    cin>>N;
    vi tw(N), ts(N);
    vll tv(N);
    rep(i,N){
        cin>>tw[i]>>ts[i]>>tv[i];
        S=max(S, ts[i]);
        W=max(W, tw[i]);
    }

    vector<P> seq(N);
    rep(i,N)seq[i]=mp(tw[i]+ts[i], i);
    sort(all(seq));
    rep(i,N){
        int ind=seq[i].se;
        w.pb(tw[ind]);
        s.pb(ts[ind]);
        v.pb(tv[ind]);
    }
}

ll dp[1010][10010];
ll ans;
void solve(){
    rep(i,N+1)rep(we,S+W+1)dp[i][we]=-1;
    dp[0][0]=0;
    rep(i,N)rep(we, S+W+1)if(dp[i][we]!=-1){
        dp[i+1][we]=max(dp[i+1][we], dp[i][we]);
        if(we<=s[i]) dp[i+1][we+w[i]]=max(dp[i+1][we+w[i]], dp[i][we]+v[i]);
    }
    rep(we,S+W+1)ans=max(ans, dp[N][we]);
}

void output(){
    cout<<ans;
}

int main(){
  input();
  solve();
  output();
}