Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Hanoi Factory

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOf 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 *a*_{i}, outer radius *b*_{i} and height *h*_{i}. 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*b*_{j}≤*b*_{i}. - Rings should not fall one into the the other. That means one can place ring
*j*on the ring*i*only if*b*_{j}>*a*_{i}. - 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* ≤ 100 000) — the number of rings in factory's stock.

The *i*-th of the next *n* lines contains three integers *a*_{i}, *b*_{i} and *h*_{i} (1 ≤ *a*_{i}, *b*_{i}, *h*_{i} ≤ 10^{9}, *b*_{i} > *a*_{i}) — 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.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/21/2017 00:34:58 (c4).

Desktop version, switch to mobile version.

User lists

Name |
---|