macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; ( iter = $ iter : ident , $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut $ iter = s . split_whitespace ( ) ; input_inner ! { $ iter , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut iter = s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; }
macro_rules ! input_inner { ( $ iter : expr ) => { } ; ( $ iter : expr , ) => { } ; ( $ iter : expr , mut $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let mut $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , mut $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , mut $ var : usize $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , $ var : usize $ ( $ r ) * } } ; }
macro_rules ! read_value { ( $ iter : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ iter , $ t ) ) ,* ) } ; ( $ iter : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ iter , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ iter : expr , { chars : $ base : expr } ) => { read_value ! ( $ iter , String ) . chars ( ) . map ( | c | ( c as u8 - $ base as u8 ) as usize ) . collect ::< Vec < usize >> ( ) } ; ( $ iter : expr , { char : $ base : expr } ) => { read_value ! ( $ iter , { chars : $ base } ) [ 0 ] } ; ( $ iter : expr , chars ) => { read_value ! ( $ iter , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ iter : expr , char ) => { read_value ! ( $ iter , chars ) [ 0 ] } ; ( $ iter : expr , usize1 ) => { read_value ! ( $ iter , usize ) - 1 } ; ( $ iter : expr , $ t : ty ) => { $ iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) } ; }
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
pub struct Adjacent {
    pub to: usize,
    pub id: usize,
}
impl Adjacent {
    pub fn new(to: usize, id: usize) -> Adjacent {
        Adjacent { to: to, id: id }
    }
}
#[derive(Clone, Debug, Default)]
pub struct Graph {
    pub vsize: usize,
    pub esize: usize,
    pub graph: Vec<Vec<Adjacent>>,
}
impl Graph {
    pub fn new(vsize: usize) -> Graph {
        Graph {
            vsize: vsize,
            esize: 0,
            graph: vec![vec![]; vsize],
        }
    }
    pub fn add_edge(&mut self, from: usize, to: usize) {
        self.graph[from].push(Adjacent::new(to, self.esize));
        self.esize += 1;
    }
    pub fn add_undirected_edge(&mut self, u: usize, v: usize) {
        self.graph[u].push(Adjacent::new(v, self.esize));
        self.graph[v].push(Adjacent::new(u, self.esize));
        self.esize += 1;
    }
    pub fn vertexes(&self) -> std::ops::Range<usize> {
        0..self.vsize
    }
    pub fn adjacency(&self, from: usize) -> &Vec<Adjacent> {
        &self.graph[from]
    }
}
#[derive(Debug)]
pub struct TreeRec {
    pub n: usize,
    pub deg: Vec<usize>,
    pub dep: (usize, usize),
}
impl TreeRec {
    pub fn new(n: usize) -> TreeRec {
        TreeRec {
            n: n,
            deg: vec![0; n],
            dep: (0, 0),
        }
    }
    pub fn init(&mut self) {
        let n = self.n;
        self.deg = vec![0; n];
        self.dep = (0, 0);
    }
    pub fn dfs(&mut self, u: usize, p: usize, d: usize, graph: &Graph) {
        let mut de = 0;
        if self.dep.0 < d {
            self.dep = (d, u);
        }
        for v in graph.adjacency(u) {
            if v.to != p {
                self.dfs(v.to, u, d + 1, graph);
                de += 1;
            }
        }
        self.deg[d] = max(self.deg[d], de);
    }
}
use std::cmp::{max, min};
fn main() {
    input! { n, ab: [(usize1, usize1); n-1] };
    let mut g = Graph::new(n);
    let mut r = TreeRec::new(n);
    for &(a, b) in &ab {
        g.add_undirected_edge(a, b);
    }
    r.dfs(0, n, 0, &g);
    let u = r.dep.1;
    r.init();
    r.dfs(u, n, 0, &g);
    let x = r.dep.0 / 2 + 1;
    let mut ans = std::usize::MAX;
    for u in 0..n {
        r.init();
        r.dfs(u, n, 0, &g);
        let mut y = 1usize;
        for i in 0..n {
            if r.deg[i] == 0 {
                break;
            }
            y = y.saturating_mul(r.deg[i]);
        }
        if r.dep.0 == x - 1 {
            ans = min(ans, y);
        }
    }
    for &(a, b) in &ab {
        r.init();
        r.dfs(a, b, 1, &g);
        r.dfs(b, a, 1, &g);
        r.deg[0] = 2;
        let mut y = 1usize;
        for i in 0..n {
            if r.deg[i] == 0 {
                break;
            }
            y = y.saturating_mul(r.deg[i]);
        }
        if r.dep.0 == x {
            ans = min(ans, y);
        }
    }
    println!("{} {}", x, ans);
}


Measured memory_bytes: 4352