PROGRAMMING:Safety production of miners

There is an underground rare metal mine, which is composed of N tunnels and some connection points. Each tunnel connects two connection points. There is at most one tunnel between any two connection points. In order to reduce the risk of absenteeism, your task is to install emergency shafts and corresponding escape devices at some connection points, so that no matter which connection point collapses, all absentees who are not at this connection point can reach the emergency shaft to escape (assuming that except for the collapsed connection point, other tunnels and connection points are intact). In order to save cost, you should install a manhole at as few connection points as possible. It is also necessary to calculate the total number of installation schemes when the number of emergency shafts is the smallest.
###Input format:
The input contains multiple sets of data. The first line of each group of data is the number of tunnels n (n < = 50000), and the following N lines have two integers in each line, that is, the number of connection points at both ends of a tunnel (all connection points are numbered from 1). All connection points of each group of data are connected. End of input with 0.
###Output format:
For each group of data, output two integers, that is, the minimum number of emergency wells to be installed and the total number of corresponding schemes. The total number of schemes is guaranteed to be within the range of 64 bit signed integers.
###Input example:
```in
nine
1 3
4 1
3 5
1 2
2 6
1 5
6 3
1 6
3 2
six
1 2
1 3
2 4
2 5
3 6
3 7
0
```
###Output example:
```out
2 4
4 1
```






answer：If there is no answer, please comment