Farmer John needs to travel to town to pick up $K$ ($1 \le K \le 10,000$) pounds of feed. Driving a mile with $K$ pounds of feed costs FJ $K*K$ cents; driving $D$ miles with $K$ pounds of feed in his truck costs FJ $D*K*K$ cents.

FJ can purchase feed from any of $N$ ($1 \le N \le 500$) stores (conveniently numbered $1..N$) that sell feed. Each store is located on a segment of the $X$ axis whose length is $E$ ($1 \le E \le 500$) miles. Store $i$ is at location $X_i$ ($0 < X_i < E$) on the number line and can sell FJ as much as $F_i$ ($1 \le F_i \le 10,000$) pounds of feed at a cost of $C_i$ ($1 \le C_i \le 10,000,000$) cents per pound. Surprisingly, a given point on the $X$ axis might have more than one store.

FJ starts driving at location 0 on this number line and can drive only in the positive direction, ultimately arriving at location $E$ with at least $K$ pounds of feed. He can stop at any of the feed stores along the way and buy any amount of feed up to the the store's limit.

What is the minimum amount FJ must pay to buy and transport the $K$ pounds of feed? FJ knows he can purchase enough feed.

Consider this example where FJ needs two pounds of feed which he must purchase from some of the three stores at locations 1, 3, and 4 on a number line whose range is 0..5:

      0   1   2   3   4   5  X
      +---|---+---|---|---+
          1       1   1      Available pounds of feed
          1       2   2      Cents per pound

It is most economical for FJ to buy one pound of feed from both the second and third stores. He must pay two cents to buy each pound of feed for a total cost of 4. FJ's driving from location 0 to location 3 costs nothing, since he is carrying no feed. When FJ travels from 3 to 4 he moves 1 mile with 1 pound of feed, so he must pay $1*1*1 = 1$ cents.

When FJ travels from 4 to 5 he moves one mile with 2 pounds of feed, so he must pay $1*2*2 = 4$ cents.

His feed cost is $2 + 2$ cents; his travel cost is $1 + 4$ cents. The total cost is $2 + 2 + 1 + 4 = 9$ cents.

TIME LIMIT: 2.5 seconds

Input

• Line 1: Three space-separated integers: $K$, $E$, and $N$

• Lines $2..N+1$: Line $i+1$ contains three space-separated integers: $X_i$, $F_i$, and $C_i$

Output

• Line 1: A single integer that is the minimum cost for FJ to buy and transport the feed

Examples

Input 1

2 5 3
3 1 2
4 1 2
1 1 1

Output 1

9

Problem credits: Tom Conerly, 2009