#include <bits/stdc++.h>
#define broken cerr << "running on " << __FUNCTION__ <<" "<< __LINE__ << endl
#define x first
#define y second
#define mp make_pair
#define sz(a) int((a).size())
#define par pair<int, int>
#define poly vector<int>
#define i64 long long
#define u64 unsigned long long
using namespace std;
const int N = 1e5 + 10, P = 998244353;
int n, cnt[N], mxd = 0, sze = 0;
vector<int> g[N];

void dfs1(int u, int fa, int dep) {
    if(dep > mxd) {
        sze = 1, mxd = dep;
    } else if(dep == mxd) {
        sze++;
    }
    for(int &v : g[u]) {
        if(v == fa) continue;
        dfs1(v, u, dep + 1);
    }
    return;
}

void dfs2(int u, int fa, int dep) {
    cnt[dep]++;
    for(int &v : g[u]) {
        if(v == fa) continue;
        dfs2(v, u, dep + 1);
    }
    return;
}

void solve() {
    cin >> n;
    for(int i = 1; i <= n; i++) g[i].clear();
    for(int i = 2, u, v; i <= n; i++) {
        cin >> u >> v;
        g[u].push_back(v), g[v].push_back(u);
    }
    mxd = sze = 0;
    for(int u = 1; u <= n; u++) {
        dfs1(u, 0, 0);
    }
    int ans = 0;
    for(int u = 1; u <= n; u++) {
        for(int i = 0; i <= mxd; i++) cnt[i] = 0;
        dfs2(u, 0, 0);
        int prod = 1;
        for(int i = 0; i <= mxd; i++) prod = 1ll * prod * cnt[i] % P;
        ans = (ans + prod) % P;
    }
    ans = (ans - sze / 2 + P) % P;
    cout << mxd + 1 <<" " << ans << endl;
    return ;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    int T;
    cin >> T;
    while(T--) solve();
    return 0;
}