#include <bits/stdc++.h>
using namespace std;

const int N = 1e3 + 3;
const int W = 1e4 + 4;
int w[N] , s[N] , v[N];
long long dp[N][W];
int idx[N];
int n;

long long solve(int i , int weight){
    if(weight >= W)return 0;
    if(i == n)return 0;
    long long &ret = dp[i][weight];
    if(~ret)return ret;
    ret = solve(i+1,weight);
    if(weight <= s[idx[i]])
        ret = max(ret , solve(i+1,weight+w[idx[i]]) + v[idx[i]]);
    return ret;
}


int main(){

    scanf("%d",&n);
    for(int i = 0 ; i < n ; i++){
        scanf("%d%d%d",&w[i],&s[i],&v[i]);
        idx[i] = i;
    }

    sort(idx,idx+n,[&](int i , int j){
            return s[i] + w[i] < s[j] + w[j];
        });

    memset(dp,-1,sizeof dp);
    printf("%lld\n",solve(0,0));

    return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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.

Examples

Input

3
2 2 20
2 1 30
3 1 40


Output

50


Input

4
1 2 10
3 1 10
2 4 10
1 6 10


Output

40


Input

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000


Output

5000000000


Input

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


Output

22

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

const int N = 1e3 + 3;
const int W = 1e4 + 4;
int w[N] , s[N] , v[N];
long long dp[N][W];
int idx[N];
int n;

long long solve(int i , int weight){
    if(weight >= W)return 0;
    if(i == n)return 0;
    long long &ret = dp[i][weight];
    if(~ret)return ret;
    ret = solve(i+1,weight);
    if(weight <= s[idx[i]])
        ret = max(ret , solve(i+1,weight+w[idx[i]]) + v[idx[i]]);
    return ret;
}


int main(){

    scanf("%d",&n);
    for(int i = 0 ; i < n ; i++){
        scanf("%d%d%d",&w[i],&s[i],&v[i]);
        idx[i] = i;
    }

    sort(idx,idx+n,[&](int i , int j){
            return s[i] + w[i] < s[j] + w[j];
        });

    memset(dp,-1,sizeof dp);
    printf("%lld\n",solve(0,0));

    return 0;
}

```