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D. Ilya and Roads

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEverything is great about Ilya's city, except the roads. The thing is, the only ZooVille road is represented as *n* holes in a row. We will consider the holes numbered from 1 to *n*, from left to right.

Ilya is really keep on helping his city. So, he wants to fix at least *k* holes (perharps he can fix more) on a single ZooVille road.

The city has *m* building companies, the *i*-th company needs *c*_{i} money units to fix a road segment containing holes with numbers of at least *l*_{i} and at most *r*_{i}. The companies in ZooVille are very greedy, so, if they fix a segment containing some already fixed holes, they do not decrease the price for fixing the segment.

Determine the minimum money Ilya will need to fix at least *k* holes.

Input

The first line contains three integers *n*, *m*, *k* (1 ≤ *n* ≤ 300, 1 ≤ *m* ≤ 10^{5}, 1 ≤ *k* ≤ *n*). The next *m* lines contain the companies' description. The *i*-th line contains three integers *l*_{i}, *r*_{i}, *c*_{i} (1 ≤ *l*_{i} ≤ *r*_{i} ≤ *n*, 1 ≤ *c*_{i} ≤ 10^{9}).

Output

Print a single integer — the minimum money Ilya needs to fix at least *k* holes.

If it is impossible to fix at least *k* holes, print -1.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

10 4 6

7 9 11

6 9 13

7 7 7

3 5 6

Output

17

Input

10 7 1

3 4 15

8 9 8

5 6 8

9 10 6

1 4 2

1 4 10

8 10 13

Output

2

Input

10 1 9

5 10 14

Output

-1

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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