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

#define fi first
#define se second
#define pb push_back
#define mp make_pair
typedef pair<int, int> ii;
typedef long long ll;

const int len = 2e4+5, mx = 1e4;
ll dp[len];
pair<ii, int> arr[len];

bool comp(pair<ii, int> a, pair<ii, int> b){
    return (a.fi.fi+a.fi.se > b.fi.fi+b.fi.se);
}

int main(){
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++)
        scanf("%d %d %d", &arr[i].fi.fi, &arr[i].fi.se, &arr[i].se);
    sort(arr+1, arr+1+n, comp);

    for (int i = 1; i <= n; i++)
        for (int j = 0; j <= mx; j++)
            if (j <= arr[i].fi.se)
                dp[j] = max(dp[j], dp[j+arr[i].fi.fi]+arr[i].se);

    printf("%lld\n", dp[0]);
    return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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;

#define fi first
#define se second
#define pb push_back
#define mp make_pair
typedef pair<int, int> ii;
typedef long long ll;

const int len = 2e4+5, mx = 1e4;
ll dp[len];
pair<ii, int> arr[len];

bool comp(pair<ii, int> a, pair<ii, int> b){
    return (a.fi.fi+a.fi.se > b.fi.fi+b.fi.se);
}

int main(){
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++)
        scanf("%d %d %d", &arr[i].fi.fi, &arr[i].fi.se, &arr[i].se);
    sort(arr+1, arr+1+n, comp);

    for (int i = 1; i <= n; i++)
        for (int j = 0; j <= mx; j++)
            if (j <= arr[i].fi.se)
                dp[j] = max(dp[j], dp[j+arr[i].fi.fi]+arr[i].se);

    printf("%lld\n", dp[0]);
    return 0;
}

```