Buggy python submission (verdict: Time Limit Exceeded):
N = 0
graphs = []

try:
    N = int(input())
    nodes = [[abs(i - j) + 1 for i in range(N)] for j in range(N)]
    for i in range(N - 1):
        line = input().split()
        u = min(int(line[0]), int(line[1])) - 1
        v = max(int(line[0]), int(line[1])) - 1
        for u2 in range(0, u + 1):
            for v2 in range(v, N):
                if u2 < v2:
                    nodes[u2][v2] -= 1
except:
  pass

a = 0
for i in range(N):
    a += sum(nodes[i][i:])
print(a)

Fixed submission:
N = 0
a = 0

try:
    N = int(input())
    for i in range(N + 1):
        a += i * (i + 1) // 2
    for i in range(N - 1):
        line = input().split()
        u = min(int(line[0]), int(line[1])) - 1
        v = max(int(line[0]), int(line[1])) - 1
        a -= (u + 1) * (N - v)        
except:
  pass

print(a)

Buggy python submission (verdict: Time Limit Exceeded):
N = 0
nodes = []

def GetReachableNodes(s, l, r):
    c = 0
    slL = None
    slR = len(nodes[s])
    for n in nodes[s]:
        if n >= l and slL == None:
            if n > r:
                break
            slL = c
        if n > r:
            slR = c
            break
        c += 1
    return [] if slL == None else nodes[s][slL:slR]

    
try:
    N = int(input())
    nodes = [[] for i in range(N)]
    for i in range(N - 1):
        line = input().split()
        u = int(line[0])
        v = int(line[1])
        nodes[u - 1].append(v - 1)
        nodes[v - 1].append(u - 1)
    for i in range(N):
        nodes[i].sort()
except:
  pass

#print(nodes)

nSubGraphs = 0
for l in range(N):
    for r in range(l, N):
        #print(l, r)
        checked = []
        for s in range(l, r + 1):
            if s not in checked:
                checked.append(s)
                #print(s)
                reachableNodes = GetReachableNodes(s, l, r)
                while len(reachableNodes) > 0:
                    nextReachableNodes = []
                    for i in reachableNodes:
                        nextReachableNodes += [n for n in GetReachableNodes(i, l, r) if n not in checked and n not in nextReachableNodes]
                    #print(reachableNodes, nextReachableNodes)
                    checked += reachableNodes
                    reachableNodes = nextReachableNodes
                nSubGraphs += 1
            
print(nSubGraphs)

Fixed submission:
N = 0
a = 0

try:
    N = int(input())
    for i in range(N + 1):
        a += i * (i + 1) // 2
    for i in range(N - 1):
        line = input().split()
        u = min(int(line[0]), int(line[1])) - 1
        v = max(int(line[0]), int(line[1])) - 1
        a -= (u + 1) * (N - v)        
except:
  pass

print(a)

Buggy python submission (verdict: Runtime Error):
N = 0
nodes = {}

try:
    N = int(input())
    for i in range(N - 1):
        line = input().split()
        u = int(line[0])
        v = int(line[1])
        if u > v:
            t = u
            u = v
            v = t
        if u - 1 in nodes:
            nodes[u - 1].append(v - 1)
        else:
            nodes[u - 1] = [v - 1]
        if v - 1 in nodes:
            nodes[v - 1].append(u - 1)
        else:
            nodes[v - 1] = [u - 1]
except:
  pass

#print(nodes)

nSubGraphs = 0
for l in range(N):
    for r in range(l, N):
        #print(l, r)
        checked = []
        for s in range(l, r + 1):
            if s not in checked:
                checked.append(s)
                #print(s)
                reachableNodes = [n for n in nodes[s] if n >= l and n <= r]
                while len(reachableNodes) > 0:
                    nextReachableNodes = []
                    for i in reachableNodes:
                        nextReachableNodes += [n for n in nodes[i] if n not in checked and n >= l and n <= r]
                    #print(reachableNodes, nextReachableNodes)
                    checked += reachableNodes
                    reachableNodes = nextReachableNodes
                nSubGraphs += 1
            
print(nSubGraphs)

Fixed submission:
N = 0
a = 0

try:
    N = int(input())
    for i in range(N + 1):
        a += i * (i + 1) // 2
    for i in range(N - 1):
        line = input().split()
        u = min(int(line[0]), int(line[1])) - 1
        v = max(int(line[0]), int(line[1])) - 1
        a -= (u + 1) * (N - v)        
except:
  pass

print(a)