City C is a very busy metropolis, and the roads in the city are very congested, so the mayor has decided to renovate them. The roads in City C are distributed as follows: there are $n$ intersections in the city, and some intersections are connected by roads. There is at most one road between any two intersections. These roads are bidirectional and connect all intersections directly or indirectly. Each road has a score; the smaller the score, the busier the road and the more it needs to be renovated. However, the municipal government has limited funds, and the mayor hopes to renovate as few roads as possible. Therefore, he has proposed the following requirements:

1. The renovated roads must be able to connect all intersections directly or indirectly.
2. Subject to requirement 1, the number of renovated roads should be as small as possible.
3. Subject to requirements 1 and 2, the maximum score among the renovated roads should be as small as possible.

Task: As a member of the city planning bureau, you should make the best decision and choose which roads should be renovated.

Input

The first line contains two integers $n$ and $m$, representing that the city has $n$ intersections and $m$ roads. The following $m$ lines describe each road, where $u, v, c$ indicate that there is a road between intersection $u$ and $v$ with a score of $c$. ($1 \le n \le 300$, $1 \le c \le 10000$)

Output

Two integers $s$ and $max$, representing the number of roads you have selected and the score of the road with the maximum score among them.

Examples

Input 1

4 5
1 2 3
1 4 5
2 4 7
2 3 6
3 4 8

Output 1

3 6