Problem: 2063C - Remove Exactly Two
Language: python

Solution 1 (runtime: 811 ms):
import sys,math,bisect,heapq
input=sys.stdin.readline
#remember file names are input.txt and output.txt 
#remember to pass only one argument to print
#add this lines before your program and after defining fast io(or that will over write testing)
#after testing done set flag =0
flag=0
if flag:
    class out:
        def __init__(self):
            self.fo=open("cp_with_python/cp/output.txt","w")
        def inu(self,*x):
            if str(type(x))!="<class 'str'>":
                x=str(x)
            self.fo.write(x)
            self.fo.write("\n")
    class inp:
        def __init__(self):
            self.fi=open("cp_with_python/cp/input.txt","r")
        def inu(self):
            return self.fi.readline()
    fy=out()
    print=fy.inu
    fx=inp()
    input=fx.inu

for _ in range(int(input())):
    n=int(input())
    #n,s1,s2=map(int,input().split())
    #a=list(map(int,input().split()))
    graph=[set() for i in range(n)]
    inc=[[i,0] for i in range(n)]
    for i in range(n-1):
        x,y=map(int,input().split())
        graph[x-1].add(y-1)
        graph[y-1].add(x-1)
        inc[x-1][1]+=1
        inc[y-1][1]+=1
    inc.sort(key=lambda x:x[1],reverse=True)
    ans=0
    if n==2:
        print(0)
    else:
        if inc[0][1]==inc[1][1]:
            if inc[0][1]==inc[2][1]:
                print(2*inc[0][1]-1)
            else:
                if inc[1][0] in graph[inc[0][0]]:
                    print(2*inc[0][1]-2)
                else:
                    print(2*inc[0][1]-1)
        else:
            for i in range(1,n):
                if inc[i][1]==inc[1][1]:
                    if inc[i][0] not in graph[inc[0][0]]:
                        print(inc[1][1]+inc[0][1]-1)
                        break
                else:
                    print(inc[0][1]+inc[1][1]-2)
                    break
            else:
                print(inc[0][1]+inc[1][1]-2)

Solution 2 (runtime: 718 ms):
import sys, math, collections, bisect, heapq, functools, itertools
sys.setrecursionlimit(10 ** 5)
inp = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = 10 ** 20
MX = 10 ** 5 + 10
orda = ord('a')
fmax = lambda x, y: (x if x > y else y)
fmin = lambda x, y: (x if x < y else y)

def solve():
    N = int(inp())
    degree = [0 for _ in range(N + 1)]
    adj = [[] for _ in range(N + 1)]

    for _ in range(N - 1):
        u, v = list(map(int, inp().split()))
        adj[u].append(v)
        adj[v].append(u)
        degree[u] += 1
        degree[v] += 1

    tmp = []

    for node in range(1, N + 1):
        tmp.append((degree[node], node))

    tmp.sort(reverse=True)
    mx = tmp[0][0]
    best = i = 0

    def get_mx_branch(a, d, node):
        a = a[:]
        d = d[:]
        current, current_mx = d[node], 0

        d[node] = 0
        for u in a[node]:
            d[u] -= 1

        for i in range(1, N + 1):
            current_mx = fmax(current_mx, d[i])

        return current + current_mx - 1

    while i < N and tmp[i][0] == mx:
        if i > 1: break
        best = fmax(best, get_mx_branch(adj, degree, tmp[i][1]))
        i += 1

    return best
    
def main():
    for _ in range(int(inp())):
        print(solve())

if __name__ == '__main__':
    main()