import heapq import random from collections import defaultdict,deque class Graph: def __init__(self,V,edges=None,graph=None,directed=False,weighted=False,inf=float("inf")): self.V=V self.directed=directed self.weighted=weighted self.inf=inf if graph!=None: self.graph=graph """ self.edges=[] for i in range(self.V): if self.weighted: for j,d in self.graph[i]: if self.directed or not self.directed and i<=j: self.edges.append((i,j,d)) else: for j in self.graph[i]: if self.directed or not self.directed and i<=j: self.edges.append((i,j)) """ else: self.edges=edges self.graph=[[] for i in range(self.V)] if weighted: for i,j,d in self.edges: self.graph[i].append((j,d)) if not self.directed: self.graph[j].append((i,d)) else: for i,j in self.edges: self.graph[i].append(j) if not self.directed: self.graph[j].append(i) def SIV_DFS(self,s,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,lowlink=False,parents=False,postorder=False,preorder=False,subtree_size=False,topological_sort=False,unweighted_dist=False,weighted_dist=False): seen=[False]*self.V finished=[False]*self.V if directed_acyclic or cycle_detection or topological_sort: dag=True if euler_tour: et=[] if linked_components: lc=[] if lowlink: order=[None]*self.V ll=[None]*self.V idx=0 if parents or cycle_detection or lowlink or subtree_size: ps=[None]*self.V if postorder or topological_sort: post=[] if preorder: pre=[] if subtree_size: ss=[1]*self.V if unweighted_dist or bipartite_graph: uwd=[self.inf]*self.V uwd[s]=0 if weighted_dist: wd=[self.inf]*self.V wd[s]=0 stack=[(s,0)] if self.weighted else [s] while stack: if self.weighted: x,d=stack.pop() else: x=stack.pop() if not seen[x]: seen[x]=True stack.append((x,d) if self.weighted else x) if euler_tour: et.append(x) if linked_components: lc.append(x) if lowlink: order[x]=idx ll[x]=idx idx+=1 if preorder: pre.append(x) for y in self.graph[x]: if self.weighted: y,d=y if not seen[y]: stack.append((y,d) if self.weighted else y) if parents or cycle_detection or lowlink or subtree_size: ps[y]=x if unweighted_dist or bipartite_graph: uwd[y]=uwd[x]+1 if weighted_dist: wd[y]=wd[x]+d elif not finished[y]: if (directed_acyclic or cycle_detection or topological_sort) and dag: dag=False if cycle_detection: cd=(y,x) elif not finished[x]: finished[x]=True if euler_tour: et.append(~x) if lowlink: bl=True for y in self.graph[x]: if self.weighted: y,d=y if ps[x]==y and bl: bl=False continue ll[x]=min(ll[x],order[y]) if x!=s: ll[ps[x]]=min(ll[ps[x]],ll[x]) if postorder or topological_sort: post.append(x) if subtree_size: for y in self.graph[x]: if self.weighted: y,d=y if y==ps[x]: continue ss[x]+=ss[y] if bipartite_graph: bg=[[],[]] for tpl in self.edges: x,y=tpl[:2] if self.weighted else tpl if uwd[x]==self.inf or uwd[y]==self.inf: continue if not uwd[x]%2^uwd[y]%2: bg=False break else: for x in range(self.V): if uwd[x]==self.inf: continue bg[uwd[x]%2].append(x) retu=() if bipartite_graph: retu+=(bg,) if cycle_detection: if dag: cd=[] else: y,x=cd cd=self.Route_Restoration(y,x,ps) retu+=(cd,) if directed_acyclic: retu+=(dag,) if euler_tour: retu+=(et,) if linked_components: retu+=(lc,) if lowlink: retu=(ll,) if parents: retu+=(ps,) if postorder: retu+=(post,) if preorder: retu+=(pre,) if subtree_size: retu+=(ss,) if topological_sort: if dag: tp_sort=post[::-1] else: tp_sort=[] retu+=(tp_sort,) if unweighted_dist: retu+=(uwd,) if weighted_dist: retu+=(wd,) if len(retu)==1: retu=retu[0] return retu def Centroid(self,root=0): x=root parents,size=self.SIV_DFS(x,parents=True,subtree_size=True) while True: for y in self.graph[x]: if self.weighted: y,d=y if y==parents[x]: continue if size[y]*2>size[root]: x=y break else: for y in self.graph[x]: if self.weighted: y,d=y if y==parents[x]: continue if size[root]<=2*size[y]: return x,y return x,None def Centroid_Decomposition(self,points=False,edges=False,tree=False,linked_point=False): if points: cd_points=[None]*self.V if edges: cd_edges=[None]*self.V if tree: cd_tree=[]*self.V if linked_point: cd_linked_point=[None]*self.V E=self.edges P=[i for i in range(self.V)] prev_centroid=None stack=[(E,P,None,prev_centroid)] if linked_point else [(E,P,prev_centroid)] while stack: if linked_point: E,P,lp,prev_centroid=stack.pop() else: E,P,prev_centroid=stack.pop() if len(P)==1: centroid=P[0] if edges: cd_edges[centroid]=[] if linked_point: cd_linked_point[centroid]=lp if points: cd_points[centroid]=[centroid] if tree and prev_centroid!=None: cd_tree.append((prev_centroid,centroid)) continue G=Graph(len(P),edges=E,weighted=self.weighted) centroid,_=G.Centroid() if tree and prev_centroid!=None: cd_tree.append((prev_centroid,P[centroid])) parents,tour=G.SIV_DFS(centroid,parents=True,preorder=True) dp=[None]*len(P) EE=[] PP=[] if linked_point: linked_points=[] for i,x in enumerate(G.graph[centroid]): if G.weighted: x,d=x dp[x]=(i,0) EE.append([]) PP.append([P[x]]) if linked_point: linked_points.append(P[x]) for x in tour[1:]: for y in G.graph[x]: if G.weighted: y,d=y if y==parents[x]: continue i,j=dp[x] jj=len(PP[i]) EE[i].append((j,jj,d) if G.weighted else (j,jj)) PP[i].append(P[y]) dp[y]=(i,jj) centroid=P[centroid] if points: cd_points[centroid]=P if edges: cd_edges[centroid]=E if linked_point: cd_linked_point[centroid]=lp if linked_point: for E,P,lp in zip(EE,PP,linked_points): stack.append((E,P,lp,centroid)) else: for E,P in zip(EE,PP): stack.append((E,P,centroid)) retu=() if points: retu+=(cd_points,) if edges: retu+=(cd_edges,) if tree: retu+=(cd_tree,) if linked_point: retu+=(cd_linked_point,) if len(retu)==1: retu=retu[0] return retu N,K=map(int,input().split()) edges=[] for i in range(N-1): u,v,c=map(int,input().split()) u-=1;v-=1 edges.append((u,v,c)) G=Graph(N,edges=edges,weighted=True) P,E,CD=G.Centroid_Decomposition(points=True,edges=True,tree=True) def solve(dp_C): cnt1=defaultdict(int) cnt2=defaultdict(int) c1=0 for tpl in dp_C: if len(tpl)==1: cnt1[tpl[0]]+=1 c1+=1 elif len(tpl)==2: a,b=tpl if a>b: a,b=b,a cnt2[(a,b)]+=1 retu=0 retu+=c1*(c1-1)//2 for c in cnt1.values(): retu-=c*(c-1)//2 for (a,b),c in cnt2.items(): retu+=c*(c-1)//2 retu+=cnt1[a]+cnt1[b] return retu ans=0 for g in range(N): r=P[g].index(g) le=len(P[g]) GG=Graph(le,E[g],weighted=True) dp_C=[None]*le dp_P=[None]*le parents,tour=GG.SIV_DFS(r,parents=True,preorder=True) dp_C[r]=tuple() for x in tour: for y,c in GG.graph[x]: if y==parents[x]: continue if len(dp_C[x])>=3 or c in dp_C[x]: dp_C[y]=dp_C[x] else: dp_C[y]=dp_C[x]+(c,) if x==r: dp_P[y]=y else: dp_P[y]=dp_P[x] tpls=[] dct=[[] for i in range(le)] for p,c in zip(dp_P,dp_C): if p==None: continue dct[p].append(c) tpls.append(c) if len(c)==2: ans+=1 ans+=solve(tpls) for lst in dct: ans-=solve(lst) print(ans)