Everything 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 ci money units to fix a road segment containing holes with numbers of at least li and at most ri. 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.
The first line contains three integers n,m,k (1≤n≤300,1≤m≤105,1≤k≤n). The next m lines contain the companies' description. The i-th line contains three integers li,ri,ci (1≤li≤ri≤n,1≤ci≤109).
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 C++. It is preferred to use the cin, cout streams or the %I64d specifier.
10 4 6
7 9 11
6 9 13
7 7 7
3 5 6
17
10 7 1
3 4 15
8 9 8
5 6 8
9 10 6
1 4 2
1 4 10
8 10 13
2
10 1 9
5 10 14
-1