Farmer John dutifully checks on the cows every day. He traverses some of the $M$ $(1 \le M \le 50,000)$ trails conveniently numbered $1,\ldots,M$ from pasture 1 all the way out to pasture $N$ (a journey which is always possible for trail maps given in the test data). The $N$ $(1 \le N \le 10,000)$ pastures conveniently numbered $1,\ldots,N$ on Farmer John's farm are currently connected by bidirectional dirt trails. Each trail $i$ connects pastures $P1_{i}$ and $P2_{i}$ $(1 \le P1_i \le N; 1 \le P2_i \le N)$ and requires $T_{i}$ $(1 \le T_{i} \le 1,000,000)$ units of time to traverse.

He wants to revamp some of the trails on his farm to save time on his long journey. Specifically, he will choose $K$ $(1 \le K \le 20)$ trails to turn into highways, which will effectively reduce the trail's traversal time to 0. Help FJ decide which trails to revamp to minimize the resulting time of getting from pasture 1 to $N$.

TIME LIMIT: 2 seconds

Input

• Line 1: Three space-separated integers: $N$, $M$, and $K$
• Lines $2,\ldots,M+1$: Line $i+1$ describes trail $i$ with three space-separated integers: $P1_{i}$, $P2_{i}$, and $T_{i}$

Output

• Line 1: The length of the shortest path after revamping no more than $K$ edges

Examples

Input 1

4 4 1
1 2 10
2 4 10
1 3 1
3 4 100

Output 1

1

$K$ is 1; revamp trail $3->4$ to take time 0 instead of 100. The new shortest path is $1->3->4$, total traversal time now 1.

Problem credits: Percy Liang, 2008