Parcel Delivery

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

$2 \le n \le 500$

$1 \le m \le 1000$

$1 \le k \le 100$

$1 \le a,b \le n$

$1 \le r,c \le 1000$

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).