There are $m$ real estate agents in the city. There is a street containing $n$ houses in a straight line and they are numbered from $1$ to $n$. The $i^{th}$ agent sells the houses with numbers from $I_i$ to $r_i$ and gets $c_i$ dollars as the commission fee. 

Note: The $i^{th}$ agent is paid either $0$ or $c_i$ dollars. 

If you want to buy a house, then you are required to pay the commission to all the agents selling that house but each agent can be paid at most once.

If you want to buy exactly $k$ houses in the city, then determine the minimum amount of money that you must pay in dollars.

Input format

• First line: Three space-separated integers $n, m,$ and $k$ denoting the number of houses, the number of agents, and the number of houses you want to buy
• Next $n$ lines: Three space-separated integers $l_i, r_i,$ and $c_i$ denoting the range of houses and the commission earned by the $i^{th}$ agent

Output format

In a single line, print one number that represents the minimum amount of money that you are required to pay to buy exactly $k$ houses.

Constraints

$1 \leq n \leq 2000\\ 1 \leq m \leq 10^{5}\\ 1 \leq k \leq n\\ 1 \leq l_i \leq r_i \leq n\\  1 \leq c_i \leq 10^{9}$