#D5934. Ilya and Roads
Ilya and Roads
Ilya and Roads
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.
Input
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).
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
inputFormat
Input
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).
outputFormat
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
样例
10 4 6
7 9 11
6 9 13
7 7 7
3 5 6
17