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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>

typedef long long int int64;

#define MAX(a,b) ((a)>(b)?(a):(b))

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

int cmp(const void *a,const void *b){
  node *p=(node *)a;
  node *q=(node *)b;
  return (p->s+p->w)-(q->s+q->w);
}

void run(void){
  int n;
  scanf("%d",&n);
  node *p=(node *)calloc(n,sizeof(node));
  int i;
  for(i=0;i<n;i++){
    int w,s,v;
    scanf("%d%d%d",&w,&s,&v);
    p[i]=(node){w,s,v};
  }
  qsort(p,n,sizeof(node),cmp);
  const int m=2*10000;
  int64 *dp=(int64 *)calloc(m+1,sizeof(int64));
  for(i=0;i<n;i++){
    for(int j=p[i].s;j>=0;j--){
      dp[j+p[i].w]=MAX(dp[j+p[i].w],dp[j]+p[i].v);
    }
  }
  int64 ans=0;
  for(i=0;i<=m;i++) ans=MAX(ans,dp[i]);
  printf("%lld\n",ans);
}

int main(void){
  run();
  return 0;
}