Problem: 2063C - Remove Exactly Two
Language: python

Solution 1 (runtime: 687 ms):
import io
import os
import sys


inf = 10 ** 18
mod = 10 ** 9 + 7

ONLINE_JUDGE = __debug__

if ONLINE_JUDGE:
    R = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline


    def _input() -> str:
        return R().decode()
else:
    R = sys.stdin.readline


    def _input() -> str:
        return R()


def get_int() -> int:
    return int(_input())


def get_str() -> str:
    return _input().strip()


def get_int_list() -> list[int]:
    return list(map(int, _input().strip().split()))


def init_matrix(n_, m_, value_=0) -> list[list]:
    return [[value_] * m_ for _ in range(n_)]


def solve() -> None:
    n = get_int()

    g = init_matrix(n, 0)
    cnt = [0] * n
    pairs = set()
    for i in range(n - 1):
        u, v = get_int_list()
        u -= 1
        v -= 1
        g[v].append(u)
        g[u].append(v)
        cnt[u] += 1
        cnt[v] += 1
        pairs.add((u, v))
        pairs.add((v, u))

    order = sorted(
        range(len(cnt)),
        key=lambda x: cnt[x],
        reverse=True,
    )
    u, v = order[:2]
    h = []
    for i in range(n):
        if cnt[i] == cnt[v]:
            h.append(i)

    if cnt[u] != cnt[v]:
        for w in h:
            if (u, w) not in pairs:
                print(cnt[u] + cnt[v] - 1)
                return

        print(cnt[u] + cnt[v] - 2)
    else:
        for i in range(len(h)):
            for j in range(i + 1, len(h)):
                if (h[i], h[j]) not in pairs:
                    print(cnt[u] + cnt[v] - 1)
                    return

        print(cnt[u] + cnt[v] - 2)


for _ in range(get_int()):
    solve()


Solution 2 (runtime: 765 ms):
import sys, os, io
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

def solve646():
    n = int(input())
    e = []
    for _ in range(n-1):
        u, v = map(int, input().split())
        u, v = u-1, v-1
        e.append([u, v])
    final_res = 0
    for _ in range(2):
        adj = [[] for _ in range(n)]
        for u, v in e:
            adj[u].append(v)
            adj[v].append(u)
        rm = [False] * n
        d = [0] * n
        for i in range(n):
            d[i] = len(adj[i])
        for _ in range(2):
            mx = u = -1
            for i in range(n):
                if not rm[i] and mx < d[i]:
                    mx = d[i]
                    u = i
            rm[u] = True
            d[u] = 0
            for v in adj[u]:
                d[v] -= 1
        res = 0
        visited = rm[:]
        def dfs(u):
            visited[u] = True
            q = [u]
            while q:
                u = q.pop()
                for v in adj[u]:
                    if not visited[v]:
                        visited[v] = True
                        q.append(v)
        for i in range(n):
            if not visited[i]:
                dfs(i)
                res += 1
        final_res = max(final_res, res)
        for i, edge in enumerate(e):
            u, v = edge
            e[i] = [n-1-u, n-1-v]
    return final_res

res_test = []
for _ in range(int(input())):
    res_test.append(solve646())
    
sys.stdout.write("\n".join(map(str, res_test))) #output all test