CSES - Parcel Delivery
• Time limit: 1.00 s
• Memory limit: 512 MB
There are $n$ cities and $m$ routes through which parcels can be carried from one city to another city. For each route, you know the maximum number of parcels and the cost of a single parcel.

You want to send $k$ parcels from Syrjälä to Lehmälä. What is the cheapest way to do that?

Input

The first input line has three integers $n$, $m$ and $k$: the number of cities, routes and parcels. The cities are numbered $1,2,\dots,n$. City $1$ is Syrjälä and city $n$ is Lehmälä.

After this, there are $m$ lines that describe the routes. Each line has four integers $a$, $b$, $r$ and $c$: there is a route from city $a$ to city $b$, at most $r$ parcels can be carried through the route, and the cost of each parcel is $c$.

Output

Print one integer: the minimum total cost or $-1$ if there are no solutions.

Constraints
• $1 \le n \le 500$
• $1 \le m \le 1000$
• $1 \le k \le 100$
• $1 \le a,b \le n$
• $1 \le r,c \le 1000$
Example

Input:
4 5 3 1 2 5 100 1 3 10 50 1 4 7 500 2 4 8 350 3 4 2 100

Output:
750

Explanation: One parcel is delivered through route $1 \rightarrow 2 \rightarrow 4$ (cost $1 \cdot 450=450$) and two parcels are delivered through route $1 \rightarrow 3 \rightarrow 4$ (cost $2 \cdot 150=300$).