Problem1520--Hanoi Factory

1520: Hanoi Factory

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Of course you have heard the famous task about Hanoi Towers, but did you know that there is a special factory producing the rings for this wonderful game? Once upon a time, the ruler of the ancient Egypt ordered the workers of Hanoi Factory to create as high tower as possible. They were not ready to serve such a strange order so they had to create this new tower using already produced rings.

There are n rings in factory's stock. The i-th ring has inner radius ai, outer radius bi and height hi. The goal is to select some subset of rings and arrange them such that the following conditions are satisfied:

  • Outer radiuses form a non-increasing sequence, i.e. one can put the j-th ring on the i-th ring only if bj≤bi.
  • Rings should not fall one into the the other. That means one can place ring j on the ring i only if bj>ai.
  • The total height of all rings used should be maximum possible.
Input

The first line of the input contains a single integer n (1≤n≤100000)− the number of rings in factory's stock.

The i-th of the next n lines contains three integers ai, bi and hi (1≤ai,bi,hi≤109, bi>ai)− inner radius, outer radius and the height of the i-th ring respectively.

Output

Print one integer− the maximum height of the tower that can be obtained.

Examples
Input
3
1 5 1
2 6 2
3 7 3
Output
6
Input
4
1 2 1
1 3 3
4 6 2
5 7 1
Output
4
Note

In the first sample, the optimal solution is to take all the rings and put them on each other in order 3, 2, 1.

In the second sample, one can put the ring 3 on the ring 4 and get the tower of height 3, or put the ring 1 on the ring 2 and get the tower of height 4.

Source/Category

 
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